1,1,192,0,0.414735," ","integrate(tan(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{150 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 300 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 400 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 200 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 15 \, {\left(a e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 46 \, a}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/15*(150*a*e^(8*I*d*x + 8*I*c) + 300*a*e^(6*I*d*x + 6*I*c) + 400*a*e^(4*I*d*x + 4*I*c) + 200*a*e^(2*I*d*x + 2*I*c) + 15*(a*e^(10*I*d*x + 10*I*c) + 5*a*e^(8*I*d*x + 8*I*c) + 10*a*e^(6*I*d*x + 6*I*c) + 10*a*e^(4*I*d*x + 4*I*c) + 5*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(2*I*d*x + 2*I*c) + 1) + 46*a)/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
2,1,158,0,0.415614," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-24 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 36 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 32 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-3 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 12 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 18 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 12 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8 i \, a}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-24*I*a*e^(6*I*d*x + 6*I*c) - 36*I*a*e^(4*I*d*x + 4*I*c) - 32*I*a*e^(2*I*d*x + 2*I*c) + (-3*I*a*e^(8*I*d*x + 8*I*c) - 12*I*a*e^(6*I*d*x + 6*I*c) - 18*I*a*e^(4*I*d*x + 4*I*c) - 12*I*a*e^(2*I*d*x + 2*I*c) - 3*I*a)*log(e^(2*I*d*x + 2*I*c) + 1) - 8*I*a)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
3,1,120,0,0.431744," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{18 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 18 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, {\left(a e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 8 \, a}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(18*a*e^(4*I*d*x + 4*I*c) + 18*a*e^(2*I*d*x + 2*I*c) + 3*(a*e^(6*I*d*x + 6*I*c) + 3*a*e^(4*I*d*x + 4*I*c) + 3*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(2*I*d*x + 2*I*c) + 1) + 8*a)/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
4,1,85,0,0.405420," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 i \, a}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(4*I*a*e^(2*I*d*x + 2*I*c) + (I*a*e^(4*I*d*x + 4*I*c) + 2*I*a*e^(2*I*d*x + 2*I*c) + I*a)*log(e^(2*I*d*x + 2*I*c) + 1) + 2*I*a)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
5,1,47,0,0.452998," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 \, a}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"-((a*e^(2*I*d*x + 2*I*c) + a)*log(e^(2*I*d*x + 2*I*c) + 1) + 2*a)/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
6,1,18,0,0.418260," ","integrate(a+I*a*tan(d*x+c),x, algorithm=""fricas"")","-\frac{i \, a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d}"," ",0,"-I*a*log(e^(2*I*d*x + 2*I*c) + 1)/d","A",0
7,1,17,0,0.428022," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d}"," ",0,"a*log(e^(2*I*d*x + 2*I*c) - 1)/d","A",0
8,1,51,0,0.454302," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 2 i \, a}{d e^{\left(2 i \, d x + 2 i \, c\right)} - d}"," ",0,"((I*a*e^(2*I*d*x + 2*I*c) - I*a)*log(e^(2*I*d*x + 2*I*c) - 1) - 2*I*a)/(d*e^(2*I*d*x + 2*I*c) - d)","A",0
9,1,83,0,0.424751," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(a e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 2 \, a}{d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(4*a*e^(2*I*d*x + 2*I*c) - (a*e^(4*I*d*x + 4*I*c) - 2*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(2*I*d*x + 2*I*c) - 1) - 2*a)/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
10,1,124,0,0.412519," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{18 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(-3 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 9 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 9 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 8 i \, a}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/3*(18*I*a*e^(4*I*d*x + 4*I*c) - 18*I*a*e^(2*I*d*x + 2*I*c) + (-3*I*a*e^(6*I*d*x + 6*I*c) + 9*I*a*e^(4*I*d*x + 4*I*c) - 9*I*a*e^(2*I*d*x + 2*I*c) + 3*I*a)*log(e^(2*I*d*x + 2*I*c) - 1) + 8*I*a)/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
11,1,156,0,0.416055," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{24 \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 36 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 32 \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, {\left(a e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 8 \, a}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/3*(24*a*e^(6*I*d*x + 6*I*c) - 36*a*e^(4*I*d*x + 4*I*c) + 32*a*e^(2*I*d*x + 2*I*c) - 3*(a*e^(8*I*d*x + 8*I*c) - 4*a*e^(6*I*d*x + 6*I*c) + 6*a*e^(4*I*d*x + 4*I*c) - 4*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(2*I*d*x + 2*I*c) - 1) - 8*a)/(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
12,1,196,0,0.418539," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-150 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 300 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 400 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 200 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(15 i \, a e^{\left(10 i \, d x + 10 i \, c\right)} - 75 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 150 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 150 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 75 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 15 i \, a\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 46 i \, a}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/15*(-150*I*a*e^(8*I*d*x + 8*I*c) + 300*I*a*e^(6*I*d*x + 6*I*c) - 400*I*a*e^(4*I*d*x + 4*I*c) + 200*I*a*e^(2*I*d*x + 2*I*c) + (15*I*a*e^(10*I*d*x + 10*I*c) - 75*I*a*e^(8*I*d*x + 8*I*c) + 150*I*a*e^(6*I*d*x + 6*I*c) - 150*I*a*e^(4*I*d*x + 4*I*c) + 75*I*a*e^(2*I*d*x + 2*I*c) - 15*I*a)*log(e^(2*I*d*x + 2*I*c) - 1) - 46*I*a)/(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)","B",0
13,1,216,0,0.425269," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-270 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 600 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 740 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 400 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 86 i \, a^{2} + {\left(-30 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} - 150 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 300 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 300 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 150 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 30 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*(-270*I*a^2*e^(8*I*d*x + 8*I*c) - 600*I*a^2*e^(6*I*d*x + 6*I*c) - 740*I*a^2*e^(4*I*d*x + 4*I*c) - 400*I*a^2*e^(2*I*d*x + 2*I*c) - 86*I*a^2 + (-30*I*a^2*e^(10*I*d*x + 10*I*c) - 150*I*a^2*e^(8*I*d*x + 8*I*c) - 300*I*a^2*e^(6*I*d*x + 6*I*c) - 300*I*a^2*e^(4*I*d*x + 4*I*c) - 150*I*a^2*e^(2*I*d*x + 2*I*c) - 30*I*a^2)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
14,1,174,0,0.423122," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 29 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 \, a^{2} + 3 \, {\left(a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)\right)}}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"2/3*(21*a^2*e^(6*I*d*x + 6*I*c) + 36*a^2*e^(4*I*d*x + 4*I*c) + 29*a^2*e^(2*I*d*x + 2*I*c) + 8*a^2 + 3*(a^2*e^(8*I*d*x + 8*I*c) + 4*a^2*e^(6*I*d*x + 6*I*c) + 6*a^2*e^(4*I*d*x + 4*I*c) + 4*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
15,1,136,0,0.419656," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 36 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 14 i \, a^{2} + {\left(6 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 18 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 18 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(30*I*a^2*e^(4*I*d*x + 4*I*c) + 36*I*a^2*e^(2*I*d*x + 2*I*c) + 14*I*a^2 + (6*I*a^2*e^(6*I*d*x + 6*I*c) + 18*I*a^2*e^(4*I*d*x + 4*I*c) + 18*I*a^2*e^(2*I*d*x + 2*I*c) + 6*I*a^2)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
16,1,93,0,0.422368," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, a^{2} + {\left(a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)\right)}}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"-2*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*a^2 + (a^2*e^(4*I*d*x + 4*I*c) + 2*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
17,1,55,0,0.435898," ","integrate((a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-2 i \, a^{2} + {\left(-2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-2*I*a^2 + (-2*I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
18,1,19,0,0.566616," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{2} \log\left(e^{\left(4 i \, d x + 4 i \, c\right)} - 1\right)}{d}"," ",0,"a^2*log(e^(4*I*d*x + 4*I*c) - 1)/d","A",0
19,1,57,0,0.412123," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-2 i \, a^{2} + {\left(2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} - d}"," ",0,"(-2*I*a^2 + (2*I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) - d)","A",0
20,1,94,0,0.423563," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, a^{2} - {\left(a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)\right)}}{d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"2*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*a^2 - (a^2*e^(4*I*d*x + 4*I*c) - 2*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
21,1,138,0,0.426274," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 36 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 14 i \, a^{2} + {\left(-6 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 18 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/3*(30*I*a^2*e^(4*I*d*x + 4*I*c) - 36*I*a^2*e^(2*I*d*x + 2*I*c) + 14*I*a^2 + (-6*I*a^2*e^(6*I*d*x + 6*I*c) + 18*I*a^2*e^(4*I*d*x + 4*I*c) - 18*I*a^2*e^(2*I*d*x + 2*I*c) + 6*I*a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
22,1,174,0,0.423552," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(21 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 36 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 29 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 8 \, a^{2} - 3 \, {\left(a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)\right)}}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-2/3*(21*a^2*e^(6*I*d*x + 6*I*c) - 36*a^2*e^(4*I*d*x + 4*I*c) + 29*a^2*e^(2*I*d*x + 2*I*c) - 8*a^2 - 3*(a^2*e^(8*I*d*x + 8*I*c) - 4*a^2*e^(6*I*d*x + 6*I*c) + 6*a^2*e^(4*I*d*x + 4*I*c) - 4*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
23,1,218,0,0.429559," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-270 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 600 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 740 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 400 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 86 i \, a^{2} + {\left(30 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} - 150 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 300 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 300 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 150 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 30 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/15*(-270*I*a^2*e^(8*I*d*x + 8*I*c) + 600*I*a^2*e^(6*I*d*x + 6*I*c) - 740*I*a^2*e^(4*I*d*x + 4*I*c) + 400*I*a^2*e^(2*I*d*x + 2*I*c) - 86*I*a^2 + (30*I*a^2*e^(10*I*d*x + 10*I*c) - 150*I*a^2*e^(8*I*d*x + 8*I*c) + 300*I*a^2*e^(6*I*d*x + 6*I*c) - 300*I*a^2*e^(4*I*d*x + 4*I*c) + 150*I*a^2*e^(2*I*d*x + 2*I*c) - 30*I*a^2)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)","B",0
24,1,214,0,0.426582," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(240 \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 585 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 695 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 385 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 83 \, a^{3} + 30 \, {\left(a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)\right)}}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"2/15*(240*a^3*e^(8*I*d*x + 8*I*c) + 585*a^3*e^(6*I*d*x + 6*I*c) + 695*a^3*e^(4*I*d*x + 4*I*c) + 385*a^3*e^(2*I*d*x + 2*I*c) + 83*a^3 + 30*(a^3*e^(10*I*d*x + 10*I*c) + 5*a^3*e^(8*I*d*x + 8*I*c) + 10*a^3*e^(6*I*d*x + 6*I*c) + 10*a^3*e^(4*I*d*x + 4*I*c) + 5*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","A",0
25,1,175,0,0.423621," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 46 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 36 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i \, a^{3} + {\left(4 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 16 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 24 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(24*I*a^3*e^(6*I*d*x + 6*I*c) + 46*I*a^3*e^(4*I*d*x + 4*I*c) + 36*I*a^3*e^(2*I*d*x + 2*I*c) + 10*I*a^3 + (4*I*a^3*e^(8*I*d*x + 8*I*c) + 16*I*a^3*e^(6*I*d*x + 6*I*c) + 24*I*a^3*e^(4*I*d*x + 4*I*c) + 16*I*a^3*e^(2*I*d*x + 2*I*c) + 4*I*a^3)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
26,1,134,0,0.417594," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(24 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 33 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 13 \, a^{3} + 6 \, {\left(a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)\right)}}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-2/3*(24*a^3*e^(4*I*d*x + 4*I*c) + 33*a^3*e^(2*I*d*x + 2*I*c) + 13*a^3 + 6*(a^3*e^(6*I*d*x + 6*I*c) + 3*a^3*e^(4*I*d*x + 4*I*c) + 3*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
27,1,95,0,0.412766," ","integrate((a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, a^{3} + {\left(-4 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-8*I*a^3*e^(2*I*d*x + 2*I*c) - 6*I*a^3 + (-4*I*a^3*e^(4*I*d*x + 4*I*c) - 8*I*a^3*e^(2*I*d*x + 2*I*c) - 4*I*a^3)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
28,1,83,0,0.436599," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} + 3 \, {\left(a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left(a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(2*a^3 + 3*(a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(2*I*d*x + 2*I*c) + 1) + (a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
29,1,90,0,0.447079," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-2 i \, a^{3} + {\left(i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left(3 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} - d}"," ",0,"(-2*I*a^3 + (I*a^3*e^(2*I*d*x + 2*I*c) - I*a^3)*log(e^(2*I*d*x + 2*I*c) + 1) + (3*I*a^3*e^(2*I*d*x + 2*I*c) - 3*I*a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) - d)","A",0
30,1,94,0,0.450168," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, a^{3} - 2 \, {\left(a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)\right)}}{d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"2*(4*a^3*e^(2*I*d*x + 2*I*c) - 3*a^3 - 2*(a^3*e^(4*I*d*x + 4*I*c) - 2*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
31,1,138,0,0.418906," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{48 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 66 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 26 i \, a^{3} + {\left(-12 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 36 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 12 i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/3*(48*I*a^3*e^(4*I*d*x + 4*I*c) - 66*I*a^3*e^(2*I*d*x + 2*I*c) + 26*I*a^3 + (-12*I*a^3*e^(6*I*d*x + 6*I*c) + 36*I*a^3*e^(4*I*d*x + 4*I*c) - 36*I*a^3*e^(2*I*d*x + 2*I*c) + 12*I*a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","A",0
32,1,174,0,0.421134," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(12 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 23 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 18 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 \, a^{3} - 2 \, {\left(a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)\right)}}{d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"-2*(12*a^3*e^(6*I*d*x + 6*I*c) - 23*a^3*e^(4*I*d*x + 4*I*c) + 18*a^3*e^(2*I*d*x + 2*I*c) - 5*a^3 - 2*(a^3*e^(8*I*d*x + 8*I*c) - 4*a^3*e^(6*I*d*x + 6*I*c) + 6*a^3*e^(4*I*d*x + 4*I*c) - 4*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
33,1,218,0,0.431968," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-480 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 1170 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 1390 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 770 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 166 i \, a^{3} + {\left(60 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 300 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 600 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 600 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 300 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 60 i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/15*(-480*I*a^3*e^(8*I*d*x + 8*I*c) + 1170*I*a^3*e^(6*I*d*x + 6*I*c) - 1390*I*a^3*e^(4*I*d*x + 4*I*c) + 770*I*a^3*e^(2*I*d*x + 2*I*c) - 166*I*a^3 + (60*I*a^3*e^(10*I*d*x + 10*I*c) - 300*I*a^3*e^(8*I*d*x + 8*I*c) + 600*I*a^3*e^(6*I*d*x + 6*I*c) - 600*I*a^3*e^(4*I*d*x + 4*I*c) + 300*I*a^3*e^(2*I*d*x + 2*I*c) - 60*I*a^3)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)","A",0
34,1,254,0,0.433591," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{4 \, {\left(270 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 855 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 1350 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 1125 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 486 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 86 \, a^{4} + 30 \, {\left(a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)\right)}}{15 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"4/15*(270*a^4*e^(10*I*d*x + 10*I*c) + 855*a^4*e^(8*I*d*x + 8*I*c) + 1350*a^4*e^(6*I*d*x + 6*I*c) + 1125*a^4*e^(4*I*d*x + 4*I*c) + 486*a^4*e^(2*I*d*x + 2*I*c) + 86*a^4 + 30*(a^4*e^(12*I*d*x + 12*I*c) + 6*a^4*e^(10*I*d*x + 10*I*c) + 15*a^4*e^(8*I*d*x + 8*I*c) + 20*a^4*e^(6*I*d*x + 6*I*c) + 15*a^4*e^(4*I*d*x + 4*I*c) + 6*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","A",0
35,1,216,0,0.423967," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{840 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 2220 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 2620 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 1460 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 316 i \, a^{4} + {\left(120 i \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 600 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 1200 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 1200 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 600 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 120 i \, a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*(840*I*a^4*e^(8*I*d*x + 8*I*c) + 2220*I*a^4*e^(6*I*d*x + 6*I*c) + 2620*I*a^4*e^(4*I*d*x + 4*I*c) + 1460*I*a^4*e^(2*I*d*x + 2*I*c) + 316*I*a^4 + (120*I*a^4*e^(10*I*d*x + 10*I*c) + 600*I*a^4*e^(8*I*d*x + 8*I*c) + 1200*I*a^4*e^(6*I*d*x + 6*I*c) + 1200*I*a^4*e^(4*I*d*x + 4*I*c) + 600*I*a^4*e^(2*I*d*x + 2*I*c) + 120*I*a^4)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
36,1,174,0,0.419965," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(30 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 63 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 50 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 14 \, a^{4} + 6 \, {\left(a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)\right)}}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-4/3*(30*a^4*e^(6*I*d*x + 6*I*c) + 63*a^4*e^(4*I*d*x + 4*I*c) + 50*a^4*e^(2*I*d*x + 2*I*c) + 14*a^4 + 6*(a^4*e^(8*I*d*x + 8*I*c) + 4*a^4*e^(6*I*d*x + 6*I*c) + 6*a^4*e^(4*I*d*x + 4*I*c) + 4*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
37,1,136,0,0.424302," ","integrate((a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-72 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 108 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 44 i \, a^{4} + {\left(-24 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 72 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 72 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 24 i \, a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-72*I*a^4*e^(4*I*d*x + 4*I*c) - 108*I*a^4*e^(2*I*d*x + 2*I*c) - 44*I*a^4 + (-24*I*a^4*e^(6*I*d*x + 6*I*c) - 72*I*a^4*e^(4*I*d*x + 4*I*c) - 72*I*a^4*e^(2*I*d*x + 2*I*c) - 24*I*a^4)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
38,1,137,0,0.435698," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{10 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 \, a^{4} + 7 \, {\left(a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + {\left(a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(10*a^4*e^(2*I*d*x + 2*I*c) + 8*a^4 + 7*(a^4*e^(4*I*d*x + 4*I*c) + 2*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) + 1) + (a^4*e^(4*I*d*x + 4*I*c) + 2*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
39,1,57,0,0.431419," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-4 i \, a^{4} + {\left(4 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, a^{4}\right)} \log\left(e^{\left(4 i \, d x + 4 i \, c\right)} - 1\right)}{d e^{\left(4 i \, d x + 4 i \, c\right)} - d}"," ",0,"(-4*I*a^4 + (4*I*a^4*e^(4*I*d*x + 4*I*c) - 4*I*a^4)*log(e^(4*I*d*x + 4*I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) - d)","A",0
40,1,138,0,0.433458," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{10 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 8 \, a^{4} - {\left(a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 7 \, {\left(a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(10*a^4*e^(2*I*d*x + 2*I*c) - 8*a^4 - (a^4*e^(4*I*d*x + 4*I*c) - 2*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) + 1) - 7*(a^4*e^(4*I*d*x + 4*I*c) - 2*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
41,1,138,0,0.424553," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{72 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 108 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 44 i \, a^{4} + {\left(-24 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 72 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 72 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 24 i \, a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/3*(72*I*a^4*e^(4*I*d*x + 4*I*c) - 108*I*a^4*e^(2*I*d*x + 2*I*c) + 44*I*a^4 + (-24*I*a^4*e^(6*I*d*x + 6*I*c) + 72*I*a^4*e^(4*I*d*x + 4*I*c) - 72*I*a^4*e^(2*I*d*x + 2*I*c) + 24*I*a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","A",0
42,1,174,0,0.424222," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(30 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 63 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 50 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 14 \, a^{4} - 6 \, {\left(a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)\right)}}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-4/3*(30*a^4*e^(6*I*d*x + 6*I*c) - 63*a^4*e^(4*I*d*x + 4*I*c) + 50*a^4*e^(2*I*d*x + 2*I*c) - 14*a^4 - 6*(a^4*e^(8*I*d*x + 8*I*c) - 4*a^4*e^(6*I*d*x + 6*I*c) + 6*a^4*e^(4*I*d*x + 4*I*c) - 4*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
43,1,218,0,0.422248," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-840 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 2220 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 2620 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 1460 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 316 i \, a^{4} + {\left(120 i \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} - 600 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 1200 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 1200 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 600 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 120 i \, a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}{15 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/15*(-840*I*a^4*e^(8*I*d*x + 8*I*c) + 2220*I*a^4*e^(6*I*d*x + 6*I*c) - 2620*I*a^4*e^(4*I*d*x + 4*I*c) + 1460*I*a^4*e^(2*I*d*x + 2*I*c) - 316*I*a^4 + (120*I*a^4*e^(10*I*d*x + 10*I*c) - 600*I*a^4*e^(8*I*d*x + 8*I*c) + 1200*I*a^4*e^(6*I*d*x + 6*I*c) - 1200*I*a^4*e^(4*I*d*x + 4*I*c) + 600*I*a^4*e^(2*I*d*x + 2*I*c) - 120*I*a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)","A",0
44,1,254,0,0.429847," ","integrate(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{4 \, {\left(270 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} - 855 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 1350 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 1125 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 486 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 86 \, a^{4} - 30 \, {\left(a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} - 6 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} - 20 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 6 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)\right)}}{15 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} - 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} - 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"4/15*(270*a^4*e^(10*I*d*x + 10*I*c) - 855*a^4*e^(8*I*d*x + 8*I*c) + 1350*a^4*e^(6*I*d*x + 6*I*c) - 1125*a^4*e^(4*I*d*x + 4*I*c) + 486*a^4*e^(2*I*d*x + 2*I*c) - 86*a^4 - 30*(a^4*e^(12*I*d*x + 12*I*c) - 6*a^4*e^(10*I*d*x + 10*I*c) + 15*a^4*e^(8*I*d*x + 8*I*c) - 20*a^4*e^(6*I*d*x + 6*I*c) + 15*a^4*e^(4*I*d*x + 4*I*c) - 6*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(2*I*d*x + 2*I*c) - 1))/(d*e^(12*I*d*x + 12*I*c) - 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) - 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) - 6*d*e^(2*I*d*x + 2*I*c) + d)","A",0
45,1,216,0,0.438188," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{66 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(264 \, d x - 3 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(396 \, d x - 84 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(264 \, d x - 98 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(66 \, d x - 68 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(36 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 144 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 216 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 144 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 36 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3 i}{12 \, {\left(a d e^{\left(10 i \, d x + 10 i \, c\right)} + 4 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 6 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 4 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/12*(66*d*x*e^(10*I*d*x + 10*I*c) + (264*d*x - 3*I)*e^(8*I*d*x + 8*I*c) + (396*d*x - 84*I)*e^(6*I*d*x + 6*I*c) + (264*d*x - 98*I)*e^(4*I*d*x + 4*I*c) + (66*d*x - 68*I)*e^(2*I*d*x + 2*I*c) + (36*I*e^(10*I*d*x + 10*I*c) + 144*I*e^(8*I*d*x + 8*I*c) + 216*I*e^(6*I*d*x + 6*I*c) + 144*I*e^(4*I*d*x + 4*I*c) + 36*I*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 3*I)/(a*d*e^(10*I*d*x + 10*I*c) + 4*a*d*e^(8*I*d*x + 8*I*c) + 6*a*d*e^(6*I*d*x + 6*I*c) + 4*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","A",0
46,1,175,0,0.443411," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-54 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 3 \, {\left(54 i \, d x + 17\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 81 \, {\left(2 i \, d x + 1\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-54 i \, d x - 65\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 24 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 3 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3}{12 \, {\left(a d e^{\left(8 i \, d x + 8 i \, c\right)} + 3 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/12*(-54*I*d*x*e^(8*I*d*x + 8*I*c) - 3*(54*I*d*x + 17)*e^(6*I*d*x + 6*I*c) - 81*(2*I*d*x + 1)*e^(4*I*d*x + 4*I*c) + (-54*I*d*x - 65)*e^(2*I*d*x + 2*I*c) + 24*(e^(8*I*d*x + 8*I*c) + 3*e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 3)/(a*d*e^(8*I*d*x + 8*I*c) + 3*a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","A",0
47,1,137,0,0.439613," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{14 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(28 \, d x - i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(14 \, d x - 10 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-8 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 16 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - i}{4 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"-1/4*(14*d*x*e^(6*I*d*x + 6*I*c) + (28*d*x - I)*e^(4*I*d*x + 4*I*c) + (14*d*x - 10*I)*e^(2*I*d*x + 2*I*c) - (-8*I*e^(6*I*d*x + 6*I*c) - 16*I*e^(4*I*d*x + 4*I*c) - 8*I*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - I)/(a*d*e^(6*I*d*x + 6*I*c) + 2*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","A",0
48,1,93,0,0.436708," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{10 i \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(10 i \, d x + 9\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1}{4 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/4*(10*I*d*x*e^(4*I*d*x + 4*I*c) + (10*I*d*x + 9)*e^(2*I*d*x + 2*I*c) - 4*(e^(4*I*d*x + 4*I*c) + e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) + 1)/(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","A",0
49,1,55,0,0.457711," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(6 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(6*d*x*e^(2*I*d*x + 2*I*c) + 4*I*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - I)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
50,1,32,0,0.411452," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, d x e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(-2*I*d*x*e^(2*I*d*x + 2*I*c) - 1)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
51,1,32,0,0.433944," ","integrate(1/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*d*x*e^(2*I*d*x + 2*I*c) + I)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
52,1,55,0,0.432113," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-6 i \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(-6*I*d*x*e^(2*I*d*x + 2*I*c) + 4*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 1)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
53,1,99,0,0.455896," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{10 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(10 \, d x - 9 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - i}{4 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} - a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"-1/4*(10*d*x*e^(4*I*d*x + 4*I*c) - (10*d*x - 9*I)*e^(2*I*d*x + 2*I*c) - (-4*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - I)/(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))","A",0
54,1,134,0,0.438795," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{14 i \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-28 i \, d x - 1\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, {\left(-7 i \, d x - 5\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 8 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, e^{\left(4 i \, d x + 4 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 1}{4 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/4*(14*I*d*x*e^(6*I*d*x + 6*I*c) + (-28*I*d*x - 1)*e^(4*I*d*x + 4*I*c) - 2*(-7*I*d*x - 5)*e^(2*I*d*x + 2*I*c) - 8*(e^(6*I*d*x + 6*I*c) - 2*e^(4*I*d*x + 4*I*c) + e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 1)/(a*d*e^(6*I*d*x + 6*I*c) - 2*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","A",0
55,1,179,0,0.439247," ","integrate(cot(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{54 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(162 \, d x - 51 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(162 \, d x - 81 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(54 \, d x - 65 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(24 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 72 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 72 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 24 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 3 i}{12 \, {\left(a d e^{\left(8 i \, d x + 8 i \, c\right)} - 3 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} - a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/12*(54*d*x*e^(8*I*d*x + 8*I*c) - (162*d*x - 51*I)*e^(6*I*d*x + 6*I*c) + (162*d*x - 81*I)*e^(4*I*d*x + 4*I*c) - (54*d*x - 65*I)*e^(2*I*d*x + 2*I*c) + (24*I*e^(8*I*d*x + 8*I*c) - 72*I*e^(6*I*d*x + 6*I*c) + 72*I*e^(4*I*d*x + 4*I*c) - 24*I*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 3*I)/(a*d*e^(8*I*d*x + 8*I*c) - 3*a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))","A",0
56,1,196,0,0.430201," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{588 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(1764 \, d x - 348 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(1764 \, d x - 753 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(588 \, d x - 587 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(-288 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 864 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 864 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 288 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 51 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i}{48 \, {\left(a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 3 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 3 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"-1/48*(588*d*x*e^(10*I*d*x + 10*I*c) + (1764*d*x - 348*I)*e^(8*I*d*x + 8*I*c) + (1764*d*x - 753*I)*e^(6*I*d*x + 6*I*c) + (588*d*x - 587*I)*e^(4*I*d*x + 4*I*c) - (-288*I*e^(10*I*d*x + 10*I*c) - 864*I*e^(8*I*d*x + 8*I*c) - 864*I*e^(6*I*d*x + 6*I*c) - 288*I*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 51*I*e^(2*I*d*x + 2*I*c) + 3*I)/(a^2*d*e^(10*I*d*x + 10*I*c) + 3*a^2*d*e^(8*I*d*x + 8*I*c) + 3*a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","A",0
57,1,151,0,0.454124," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{124 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 8 \, {\left(-31 i \, d x - 6\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(124 i \, d x + 95\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 64 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 2 \, e^{\left(6 i \, d x + 6 i \, c\right)} + e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 14 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1}{16 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 2 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/16*(124*I*d*x*e^(8*I*d*x + 8*I*c) - 8*(-31*I*d*x - 6)*e^(6*I*d*x + 6*I*c) + (124*I*d*x + 95)*e^(4*I*d*x + 4*I*c) - 64*(e^(8*I*d*x + 8*I*c) + 2*e^(6*I*d*x + 6*I*c) + e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) + 14*e^(2*I*d*x + 2*I*c) - 1)/(a^2*d*e^(8*I*d*x + 8*I*c) + 2*a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","A",0
58,1,111,0,0.416832," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{68 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(68 \, d x - 44 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(32 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 32 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 11 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{16 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/16*(68*d*x*e^(6*I*d*x + 6*I*c) + (68*d*x - 44*I)*e^(4*I*d*x + 4*I*c) + (32*I*e^(6*I*d*x + 6*I*c) + 32*I*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 11*I*e^(2*I*d*x + 2*I*c) + I)/(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","A",0
59,1,66,0,0.421164," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-28 i \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 16 \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(-28*I*d*x*e^(4*I*d*x + 4*I*c) + 16*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 8*e^(2*I*d*x + 2*I*c) + 1)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
60,1,43,0,0.422670," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"-1/16*(4*d*x*e^(4*I*d*x + 4*I*c) - 4*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
61,1,32,0,0.418221," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-4 i \, d x e^{\left(4 i \, d x + 4 i \, c\right)} - 1\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(-4*I*d*x*e^(4*I*d*x + 4*I*c) - 1)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
62,1,43,0,0.420608," ","integrate(1/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*d*x*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
63,1,66,0,0.437259," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-28 i \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 16 \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(-28*I*d*x*e^(4*I*d*x + 4*I*c) + 16*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 8*e^(2*I*d*x + 2*I*c) + 1)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
64,1,114,0,0.568542," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{68 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(68 \, d x - 44 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - {\left(-32 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 32 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 11 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i}{16 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"-1/16*(68*d*x*e^(6*I*d*x + 6*I*c) - (68*d*x - 44*I)*e^(4*I*d*x + 4*I*c) - (-32*I*e^(6*I*d*x + 6*I*c) + 32*I*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 11*I*e^(2*I*d*x + 2*I*c) - I)/(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))","A",0
65,1,151,0,0.422394," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{124 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 8 \, {\left(31 i \, d x + 6\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(124 i \, d x + 95\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 64 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} - 2 \, e^{\left(6 i \, d x + 6 i \, c\right)} + e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 14 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1}{16 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} - 2 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/16*(124*I*d*x*e^(8*I*d*x + 8*I*c) - 8*(31*I*d*x + 6)*e^(6*I*d*x + 6*I*c) + (124*I*d*x + 95)*e^(4*I*d*x + 4*I*c) - 64*(e^(8*I*d*x + 8*I*c) - 2*e^(6*I*d*x + 6*I*c) + e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 14*e^(2*I*d*x + 2*I*c) - 1)/(a^2*d*e^(8*I*d*x + 8*I*c) - 2*a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","A",0
66,1,164,0,0.453696," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{1332 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(2664 \, d x - 618 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(1332 \, d x - 1017 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(672 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 1344 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 672 i \, e^{\left(6 i \, d x + 6 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 182 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 23 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i}{96 \, {\left(a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 2 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)}\right)}}"," ",0,"1/96*(1332*d*x*e^(10*I*d*x + 10*I*c) + (2664*d*x - 618*I)*e^(8*I*d*x + 8*I*c) + (1332*d*x - 1017*I)*e^(6*I*d*x + 6*I*c) + (672*I*e^(10*I*d*x + 10*I*c) + 1344*I*e^(8*I*d*x + 8*I*c) + 672*I*e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 182*I*e^(4*I*d*x + 4*I*c) + 23*I*e^(2*I*d*x + 2*I*c) - 2*I)/(a^3*d*e^(10*I*d*x + 10*I*c) + 2*a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))","A",0
67,1,120,0,0.439908," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-588 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 6 \, {\left(98 i \, d x + 55\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 288 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + e^{\left(6 i \, d x + 6 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 117 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 19 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2}{96 \, {\left(a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)}\right)}}"," ",0,"1/96*(-588*I*d*x*e^(8*I*d*x + 8*I*c) - 6*(98*I*d*x + 55)*e^(6*I*d*x + 6*I*c) + 288*(e^(8*I*d*x + 8*I*c) + e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 117*e^(4*I*d*x + 4*I*c) + 19*e^(2*I*d*x + 2*I*c) - 2)/(a^3*d*e^(8*I*d*x + 8*I*c) + a^3*d*e^(6*I*d*x + 6*I*c))","A",0
68,1,77,0,0.424931," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(180 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 96 i \, e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 66 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(180*d*x*e^(6*I*d*x + 6*I*c) + 96*I*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 66*I*e^(4*I*d*x + 4*I*c) + 15*I*e^(2*I*d*x + 2*I*c) - 2*I)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
69,1,54,0,0.477563," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 i \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 18 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 9 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(12*I*d*x*e^(6*I*d*x + 6*I*c) + 18*e^(4*I*d*x + 4*I*c) - 9*e^(2*I*d*x + 2*I*c) + 2)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
70,1,54,0,0.429085," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} - 6 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"-1/96*(12*d*x*e^(6*I*d*x + 6*I*c) - 6*I*e^(4*I*d*x + 4*I*c) - 3*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
71,1,54,0,0.417531," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-12 i \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(-12*I*d*x*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) - 3*e^(2*I*d*x + 2*I*c) - 2)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
72,1,54,0,0.426883," ","integrate(1/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 9 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(12*d*x*e^(6*I*d*x + 6*I*c) + 18*I*e^(4*I*d*x + 4*I*c) + 9*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
73,1,77,0,0.428936," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-180 i \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 96 \, e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 66 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(-180*I*d*x*e^(6*I*d*x + 6*I*c) + 96*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 66*e^(4*I*d*x + 4*I*c) + 15*e^(2*I*d*x + 2*I*c) + 2)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
74,1,125,0,0.436606," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{588 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(588 \, d x - 330 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(-288 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 288 i \, e^{\left(6 i \, d x + 6 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 117 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 19 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i}{96 \, {\left(a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} - a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)}\right)}}"," ",0,"-1/96*(588*d*x*e^(8*I*d*x + 8*I*c) - (588*d*x - 330*I)*e^(6*I*d*x + 6*I*c) - (-288*I*e^(8*I*d*x + 8*I*c) + 288*I*e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 117*I*e^(4*I*d*x + 4*I*c) - 19*I*e^(2*I*d*x + 2*I*c) - 2*I)/(a^3*d*e^(8*I*d*x + 8*I*c) - a^3*d*e^(6*I*d*x + 6*I*c))","A",0
75,1,134,0,0.435942," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3096 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(3096 \, d x - 1632 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(-1536 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 1536 i \, e^{\left(8 i \, d x + 8 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 684 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 148 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 29 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i}{384 \, {\left(a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)}\right)}}"," ",0,"-1/384*(3096*d*x*e^(10*I*d*x + 10*I*c) + (3096*d*x - 1632*I)*e^(8*I*d*x + 8*I*c) - (-1536*I*e^(10*I*d*x + 10*I*c) - 1536*I*e^(8*I*d*x + 8*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 684*I*e^(6*I*d*x + 6*I*c) + 148*I*e^(4*I*d*x + 4*I*c) - 29*I*e^(2*I*d*x + 2*I*c) + 3*I)/(a^4*d*e^(10*I*d*x + 10*I*c) + a^4*d*e^(8*I*d*x + 8*I*c))","A",0
76,1,88,0,0.451498," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(248 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 128 \, e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 104 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 32 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{128 \, a^{4} d}"," ",0,"1/128*(248*I*d*x*e^(8*I*d*x + 8*I*c) - 128*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 104*e^(6*I*d*x + 6*I*c) - 32*e^(4*I*d*x + 4*I*c) + 8*e^(2*I*d*x + 2*I*c) - 1)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
77,1,65,0,0.437867," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(24 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 48 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(24*d*x*e^(8*I*d*x + 8*I*c) - 48*I*e^(6*I*d*x + 6*I*c) + 36*I*e^(4*I*d*x + 4*I*c) - 16*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
78,1,54,0,0.421255," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(24 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} + 24 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(24*I*d*x*e^(8*I*d*x + 8*I*c) + 24*e^(6*I*d*x + 6*I*c) - 8*e^(2*I*d*x + 2*I*c) + 3)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
79,1,43,0,0.415202," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{{\left(8 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{128 \, a^{4} d}"," ",0,"-1/128*(8*d*x*e^(8*I*d*x + 8*I*c) - 4*I*e^(4*I*d*x + 4*I*c) + I)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
80,1,54,0,0.421795," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(-24 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} + 24 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(-24*I*d*x*e^(8*I*d*x + 8*I*c) + 24*e^(6*I*d*x + 6*I*c) - 8*e^(2*I*d*x + 2*I*c) - 3)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
81,1,65,0,0.422262," ","integrate(1/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(24 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} + 48 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(24*d*x*e^(8*I*d*x + 8*I*c) + 48*I*e^(6*I*d*x + 6*I*c) + 36*I*e^(4*I*d*x + 4*I*c) + 16*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
82,1,88,0,0.443662," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(-248 i \, d x e^{\left(8 i \, d x + 8 i \, c\right)} + 128 \, e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) + 104 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 32 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{128 \, a^{4} d}"," ",0,"1/128*(-248*I*d*x*e^(8*I*d*x + 8*I*c) + 128*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) - 1) + 104*e^(6*I*d*x + 6*I*c) + 32*e^(4*I*d*x + 4*I*c) + 8*e^(2*I*d*x + 2*I*c) + 1)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
83,1,136,0,0.435253," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3096 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} - {\left(3096 \, d x - 1632 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} - {\left(-1536 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 1536 i \, e^{\left(8 i \, d x + 8 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right) - 684 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 148 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 29 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i}{384 \, {\left(a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} - a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)}\right)}}"," ",0,"-1/384*(3096*d*x*e^(10*I*d*x + 10*I*c) - (3096*d*x - 1632*I)*e^(8*I*d*x + 8*I*c) - (-1536*I*e^(10*I*d*x + 10*I*c) + 1536*I*e^(8*I*d*x + 8*I*c))*log(e^(2*I*d*x + 2*I*c) - 1) - 684*I*e^(6*I*d*x + 6*I*c) - 148*I*e^(4*I*d*x + 4*I*c) - 29*I*e^(2*I*d*x + 2*I*c) - 3*I)/(a^4*d*e^(10*I*d*x + 10*I*c) - a^4*d*e^(8*I*d*x + 8*I*c))","A",0
84,1,329,0,0.442221," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""fricas"")","\frac{210 \, \sqrt{2} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 210 \, \sqrt{2} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(736 i \, e^{\left(7 i \, d x + 7 i \, c\right)} + 896 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 1120 i \, e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}{420 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/420*(210*sqrt(2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a/d^2)*log(4*((I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 210*sqrt(2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a/d^2)*log(4*((-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(736*I*e^(7*I*d*x + 7*I*c) + 896*I*e^(5*I*d*x + 5*I*c) + 1120*I*e^(3*I*d*x + 3*I*c)))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
85,1,285,0,0.444233," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 15 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{d^{2}}} \log\left(-4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(17 \, e^{\left(5 i \, d x + 5 i \, c\right)} + 20 \, e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, e^{\left(i \, d x + i \, c\right)}\right)}}{30 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/30*(15*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/d^2)*log(4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 15*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/d^2)*log(-4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(17*e^(5*I*d*x + 5*I*c) + 20*e^(3*I*d*x + 3*I*c) + 15*e^(I*d*x + I*c)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
86,1,233,0,0.435572," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""fricas"")","-\frac{6 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 6 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 16 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(3 i \, d x + 3 i \, c\right)}}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/12*(6*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a/d^2)*log(4*((I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 6*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a/d^2)*log(4*((-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 16*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(3*I*d*x + 3*I*c))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
87,1,187,0,0.471537," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""fricas"")","-\frac{\sqrt{2} d \sqrt{\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} d \sqrt{\frac{a}{d^{2}}} \log\left(-4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)}}{2 \, d}"," ",0,"-1/2*(sqrt(2)*d*sqrt(a/d^2)*log(4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*d*sqrt(a/d^2)*log(-4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c))/d","B",0
88,1,159,0,0.424847," ","integrate((a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)"," ",0,"1/2*sqrt(2)*sqrt(-a/d^2)*log(4*((I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 1/2*sqrt(2)*sqrt(-a/d^2)*log(4*((-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c))","B",0
89,1,336,0,0.449576," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \sqrt{\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{a}{d^{2}}} \log\left(-4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \frac{1}{2} \, \sqrt{\frac{a}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \frac{1}{2} \, \sqrt{\frac{a}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)"," ",0,"1/2*sqrt(2)*sqrt(a/d^2)*log(4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 1/2*sqrt(2)*sqrt(a/d^2)*log(-4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 1/2*sqrt(a/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a^2)*e^(-2*I*d*x - 2*I*c)) + 1/2*sqrt(a/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a^2)*e^(-2*I*d*x - 2*I*c))","B",0
90,1,476,0,0.447269," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 2 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left({\left(48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{2} {\left(32 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 32 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a}{d^{2}}} \log\left({\left(48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{2} {\left(-32 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 32 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-4 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, e^{\left(i \, d x + i \, c\right)}\right)}}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"-1/4*(2*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a/d^2)*log(4*((I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 2*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a/d^2)*log(4*((-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a/d^2)*log((48*a^2*e^(2*I*d*x + 2*I*c) + sqrt(2)*(32*I*a*d*e^(3*I*d*x + 3*I*c) + 32*I*a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a/d^2)*log((48*a^2*e^(2*I*d*x + 2*I*c) + sqrt(2)*(-32*I*a*d*e^(3*I*d*x + 3*I*c) - 32*I*a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-4*I*e^(3*I*d*x + 3*I*c) - 4*I*e^(I*d*x + I*c)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
91,1,519,0,0.482334," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{d^{2}}} \log\left(4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 8 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{d^{2}}} \log\left(-4 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 7 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 7 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{a}{d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(3 \, e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)}}{16 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/16*(8*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/d^2)*log(4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 8*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/d^2)*log(-4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 7*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a^2)*e^(-2*I*d*x - 2*I*c)) + 7*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(a/d^2) + a^2)*e^(-2*I*d*x - 2*I*c)) - 4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(3*e^(5*I*d*x + 5*I*c) + 4*e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
92,1,354,0,0.460050," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 105 \, \sqrt{2} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 2 \, \sqrt{2} {\left(211 \, a e^{\left(7 i \, d x + 7 i \, c\right)} + 371 \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 385 \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 105 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{105 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/105*(105*sqrt(2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 105*sqrt(2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 2*sqrt(2)*(211*a*e^(7*I*d*x + 7*I*c) + 371*a*e^(5*I*d*x + 5*I*c) + 385*a*e^(3*I*d*x + 3*I*c) + 105*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
93,1,315,0,0.448416," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 20 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - \sqrt{2} {\left(-72 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} - 80 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 40 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{20 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/20*(20*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 20*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - sqrt(2)*(-72*I*a*e^(5*I*d*x + 5*I*c) - 80*I*a*e^(3*I*d*x + 3*I*c) - 40*I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
94,1,258,0,0.437155," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 3 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 2 \, \sqrt{2} {\left(5 \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/3*(3*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 3*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 2*sqrt(2)*(5*a*e^(3*I*d*x + 3*I*c) + 3*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
95,1,216,0,0.440039," ","integrate((a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{8 i \, \sqrt{2} a \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} + 4 \, \sqrt{2} \sqrt{-\frac{a^{3}}{d^{2}}} d \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 4 \, \sqrt{2} \sqrt{-\frac{a^{3}}{d^{2}}} d \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right)}{4 \, d}"," ",0,"1/4*(8*I*sqrt(2)*a*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) + 4*sqrt(2)*sqrt(-a^3/d^2)*d*log(4*(a^2*e^(I*d*x + I*c) + (I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 4*sqrt(2)*sqrt(-a^3/d^2)*d*log(4*(a^2*e^(I*d*x + I*c) + (-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a))/d","B",0
96,1,357,0,0.454697," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\sqrt{2} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - \sqrt{2} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - \frac{1}{2} \, \sqrt{\frac{a^{3}}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \frac{1}{2} \, \sqrt{\frac{a^{3}}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)"," ",0,"sqrt(2)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - sqrt(2)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 1/2*sqrt(a^3/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 1/2*sqrt(a^3/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + a^2)*e^(-2*I*d*x - 2*I*c))","B",0
97,1,501,0,0.448989," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 4 \, \sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \log\left({\left(48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{2} {\left(32 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 32 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \log\left({\left(48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{2} {\left(-32 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 32 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \sqrt{2} {\left(-4 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"-1/4*(4*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 4*sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a^3/d^2)*log((48*a^2*e^(2*I*d*x + 2*I*c) + sqrt(2)*(32*I*d*e^(3*I*d*x + 3*I*c) + 32*I*d*e^(I*d*x + I*c))*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) + 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-a^3/d^2)*log((48*a^2*e^(2*I*d*x + 2*I*c) + sqrt(2)*(-32*I*d*e^(3*I*d*x + 3*I*c) - 32*I*d*e^(I*d*x + I*c))*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) - sqrt(2)*(-4*I*a*e^(3*I*d*x + 3*I*c) - 4*I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
98,1,546,0,0.451135," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{16 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 16 \, \sqrt{2} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(\frac{4 \, {\left(a^{2} e^{\left(i \, d x + i \, c\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - 11 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 11 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a^{3}}{d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, \sqrt{2} {\left(7 \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{16 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/16*(16*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 16*sqrt(2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(4*(a^2*e^(I*d*x + I*c) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a) - 11*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 11*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a^3/d^2)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + a^2)*e^(-2*I*d*x - 2*I*c)) - 4*sqrt(2)*(7*a*e^(5*I*d*x + 5*I*c) + 4*a*e^(3*I*d*x + 3*I*c) - 3*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
99,1,412,0,0.451584," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 315 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 2 \, \sqrt{2} {\left(646 \, a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} + 1647 \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 2331 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 1365 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 315 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)}}{315 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"2/315*(315*sqrt(2)*sqrt(a^5/d^2)*(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 315*sqrt(2)*sqrt(a^5/d^2)*(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) - sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 2*sqrt(2)*(646*a^2*e^(9*I*d*x + 9*I*c) + 1647*a^2*e^(7*I*d*x + 7*I*c) + 2331*a^2*e^(5*I*d*x + 5*I*c) + 1365*a^2*e^(3*I*d*x + 3*I*c) + 315*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
100,1,371,0,0.462328," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{168 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 168 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - \sqrt{2} {\left(-640 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 1232 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 1120 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 336 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{84 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/84*(168*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 168*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - sqrt(2)*(-640*I*a^2*e^(7*I*d*x + 7*I*c) - 1232*I*a^2*e^(5*I*d*x + 5*I*c) - 1120*I*a^2*e^(3*I*d*x + 3*I*c) - 336*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
101,1,312,0,0.441048," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 15 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 2 \, \sqrt{2} {\left(26 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 35 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)}}{15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-2/15*(15*sqrt(2)*sqrt(a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 15*sqrt(2)*sqrt(a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) - sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 2*sqrt(2)*(26*a^2*e^(5*I*d*x + 5*I*c) + 35*a^2*e^(3*I*d*x + 3*I*c) + 15*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
102,1,270,0,0.436707," ","integrate((a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{24 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 24 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) + \sqrt{2} {\left(64 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 48 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/12*(24*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 24*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) + sqrt(2)*(64*I*a^2*e^(3*I*d*x + 3*I*c) + 48*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
103,1,406,0,0.439515," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} a^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} - 4 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} d \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) + 4 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} d \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) + \sqrt{\frac{a^{5}}{d^{2}}} d \log\left(\frac{16 \, {\left(3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} + 2 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - \sqrt{\frac{a^{5}}{d^{2}}} d \log\left(\frac{16 \, {\left(3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} - 2 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right)}{2 \, d}"," ",0,"-1/2*(4*sqrt(2)*a^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) - 4*sqrt(2)*sqrt(a^5/d^2)*d*log(4*(a^3*e^(I*d*x + I*c) + sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) + 4*sqrt(2)*sqrt(a^5/d^2)*d*log(4*(a^3*e^(I*d*x + I*c) - sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) + sqrt(a^5/d^2)*d*log(16*(3*a^3*e^(2*I*d*x + 2*I*c) + a^3 + 2*sqrt(2)*sqrt(a^5/d^2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) - sqrt(a^5/d^2)*d*log(16*(3*a^3*e^(2*I*d*x + 2*I*c) + a^3 - 2*sqrt(2)*sqrt(a^5/d^2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a))/d","B",0
104,1,511,0,0.520987," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 8 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 5 \, \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(48 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{3} + \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(32 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 32 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) + 5 \, \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(48 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{3} + \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-32 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 32 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - \sqrt{2} {\left(-4 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"-1/4*(8*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 8*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 5*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((48*a^3*e^(2*I*d*x + 2*I*c) + 16*a^3 + sqrt(2)*sqrt(-a^5/d^2)*(32*I*d*e^(3*I*d*x + 3*I*c) + 32*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) + 5*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((48*a^3*e^(2*I*d*x + 2*I*c) + 16*a^3 + sqrt(2)*sqrt(-a^5/d^2)*(-32*I*d*e^(3*I*d*x + 3*I*c) - 32*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) - sqrt(2)*(-4*I*a^2*e^(3*I*d*x + 3*I*c) - 4*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
105,1,558,0,0.456317," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{32 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 32 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 23 \, \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{16 \, {\left(3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} + 2 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) + 23 \, \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{16 \, {\left(3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} - 2 \, \sqrt{2} \sqrt{\frac{a^{5}}{d^{2}}} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} + d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - 4 \, \sqrt{2} {\left(11 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 7 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{16 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/16*(32*sqrt(2)*sqrt(a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 32*sqrt(2)*sqrt(a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^3*e^(I*d*x + I*c) - sqrt(a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 23*sqrt(a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(16*(3*a^3*e^(2*I*d*x + 2*I*c) + a^3 + 2*sqrt(2)*sqrt(a^5/d^2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) + 23*sqrt(a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(16*(3*a^3*e^(2*I*d*x + 2*I*c) + a^3 - 2*sqrt(2)*sqrt(a^5/d^2)*(d*e^(3*I*d*x + 3*I*c) + d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) - 4*sqrt(2)*(11*a^2*e^(5*I*d*x + 5*I*c) + 4*a^2*e^(3*I*d*x + 3*I*c) - 7*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
106,1,661,0,0.468340," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{192 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 192 \, \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{4 \, {\left(a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - 135 \, \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(384 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 128 \, a^{3} + \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(256 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 256 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a}\right) + 135 \, \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(384 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 128 \, a^{3} + \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-256 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 256 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a}\right) + 4 \, \sqrt{2} {\left(91 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 7 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 59 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 39 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{96 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/96*(192*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 192*sqrt(2)*sqrt(-a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(4*(a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 135*sqrt(-a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(1/8*(384*a^3*e^(2*I*d*x + 2*I*c) + 128*a^3 + sqrt(2)*sqrt(-a^5/d^2)*(256*I*d*e^(3*I*d*x + 3*I*c) + 256*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) + 135*sqrt(-a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(1/8*(384*a^3*e^(2*I*d*x + 2*I*c) + 128*a^3 + sqrt(2)*sqrt(-a^5/d^2)*(-256*I*d*e^(3*I*d*x + 3*I*c) - 256*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/a) + 4*sqrt(2)*(91*I*a^2*e^(7*I*d*x + 7*I*c) - 7*I*a^2*e^(5*I*d*x + 5*I*c) - 59*I*a^2*e^(3*I*d*x + 3*I*c) + 39*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
107,1,320,0,0.468127," ","integrate((a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{240 \, \sqrt{2} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{7}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3}}\right) - 240 \, \sqrt{2} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{4 \, {\left(a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{7}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3}}\right) + \sqrt{2} {\left(736 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} + 1120 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} + 480 i \, a^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{60 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/60*(240*sqrt(2)*sqrt(-a^7/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^4*e^(I*d*x + I*c) + sqrt(-a^7/d^2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) - 240*sqrt(2)*sqrt(-a^7/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(4*(a^4*e^(I*d*x + I*c) + sqrt(-a^7/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) + sqrt(2)*(736*I*a^3*e^(5*I*d*x + 5*I*c) + 1120*I*a^3*e^(3*I*d*x + 3*I*c) + 480*I*a^3*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
108,1,389,0,0.459965," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} + 3 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 105 \, \sqrt{2} {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} + 3 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(353 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 1708 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2030 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 1260 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 105\right)}}{420 \, {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} + 3 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"-1/420*(105*sqrt(2)*(a*d*e^(7*I*d*x + 7*I*c) + 3*a*d*e^(5*I*d*x + 5*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 105*sqrt(2)*(a*d*e^(7*I*d*x + 7*I*c) + 3*a*d*e^(5*I*d*x + 5*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(353*e^(8*I*d*x + 8*I*c) + 1708*e^(6*I*d*x + 6*I*c) + 2030*e^(4*I*d*x + 4*I*c) + 1260*e^(2*I*d*x + 2*I*c) + 105))/(a*d*e^(7*I*d*x + 7*I*c) + 3*a*d*e^(5*I*d*x + 5*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
109,1,340,0,0.458069," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-15 i \, a d e^{\left(5 i \, d x + 5 i \, c\right)} - 30 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 15 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} {\left(15 i \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 30 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 15 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(206 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 410 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 330 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 30 i\right)}}{60 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/60*(sqrt(2)*(-15*I*a*d*e^(5*I*d*x + 5*I*c) - 30*I*a*d*e^(3*I*d*x + 3*I*c) - 15*I*a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*(15*I*a*d*e^(5*I*d*x + 5*I*c) + 30*I*a*d*e^(3*I*d*x + 3*I*c) + 15*I*a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(206*I*e^(6*I*d*x + 6*I*c) + 410*I*e^(4*I*d*x + 4*I*c) + 330*I*e^(2*I*d*x + 2*I*c) + 30*I))/(a*d*e^(5*I*d*x + 5*I*c) + 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
110,1,289,0,0.435705," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(7 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 18 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)}}{12 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/12*(3*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(7*e^(4*I*d*x + 4*I*c) + 18*e^(2*I*d*x + 2*I*c) + 3))/(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
111,1,237,0,0.438112," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(i \, \sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - i \, \sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-10 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(I*sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - I*sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-10*I*e^(2*I*d*x + 2*I*c) - 2*I))*e^(-I*d*x - I*c)/(a*d)","B",0
112,1,235,0,0.440868," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1))*e^(-I*d*x - I*c)/(a*d)","B",0
113,1,237,0,0.455054," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(-i \, \sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + i \, \sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(-I*sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + I*sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(2*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-I*d*x - I*c)/(a*d)","B",0
114,1,459,0,0.472397," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 2 \, a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 2 \, a d \sqrt{\frac{1}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 2*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) + a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 2*a*d*sqrt(1/(a*d^2))*e^(I*d*x + I*c)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) + a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1))*e^(-I*d*x - I*c)/(a*d)","B",0
115,1,545,0,0.462374," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} {\left(-i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + {\left(i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + {\left(-i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-6 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}}{4 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/4*(sqrt(2)*(I*a*d*e^(3*I*d*x + 3*I*c) - I*a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*(-I*a*d*e^(3*I*d*x + 3*I*c) + I*a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + (I*a*d*e^(3*I*d*x + 3*I*c) - I*a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) + a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + (-I*a*d*e^(3*I*d*x + 3*I*c) + I*a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) + a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-6*I*e^(4*I*d*x + 4*I*c) - 4*I*e^(2*I*d*x + 2*I*c) + 2*I))/(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))","B",0
116,1,617,0,0.460033," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 4 \, \sqrt{2} {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(-4 \, {\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 11 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 11 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{1}{a d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(3 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 7 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2\right)}}{16 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"-1/16*(4*sqrt(2)*(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 4*sqrt(2)*(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(-4*((a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 11*(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) + a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 11*(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(1/(a*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) + a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(3*e^(6*I*d*x + 6*I*c) - 6*e^(4*I*d*x + 4*I*c) - 7*e^(2*I*d*x + 2*I*c) + 2))/(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
117,1,388,0,0.458029," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} + 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 15 \, \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} + 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(466 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 1105 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 855 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 115 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 5\right)}}{60 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} + 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"-1/60*(15*sqrt(1/2)*(a^2*d*e^(7*I*d*x + 7*I*c) + 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 15*sqrt(1/2)*(a^2*d*e^(7*I*d*x + 7*I*c) + 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(466*e^(8*I*d*x + 8*I*c) + 1105*e^(6*I*d*x + 6*I*c) + 855*e^(4*I*d*x + 4*I*c) + 115*e^(2*I*d*x + 2*I*c) - 5))/(a^2*d*e^(7*I*d*x + 7*I*c) + 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))","B",0
118,1,333,0,0.437165," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(-3 i \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 3 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{\frac{1}{2}} {\left(3 i \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-52 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 87 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{12 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/12*(sqrt(1/2)*(-3*I*a^2*d*e^(5*I*d*x + 5*I*c) - 3*I*a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(1/2)*(3*I*a^2*d*e^(5*I*d*x + 5*I*c) + 3*I*a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-52*I*e^(6*I*d*x + 6*I*c) - 87*I*e^(4*I*d*x + 4*I*c) - 18*I*e^(2*I*d*x + 2*I*c) + I))/(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))","B",0
119,1,273,0,0.439393," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(38 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 13 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(38*e^(4*I*d*x + 4*I*c) + 13*e^(2*I*d*x + 2*I*c) - 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
120,1,272,0,0.443877," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(8 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(8*I*e^(4*I*d*x + 4*I*c) + 7*I*e^(2*I*d*x + 2*I*c) - I))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
121,1,271,0,0.468230," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(2 \, e^{\left(4 i \, d x + 4 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(2*e^(4*I*d*x + 4*I*c) + e^(2*I*d*x + 2*I*c) - 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
122,1,272,0,0.435637," ","integrate(1/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(-3 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(-3*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(4*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(2*I*d*x + 2*I*c) + I))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
123,1,500,0,0.436607," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 6 \, a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 6 \, a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 6*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 6*a^2*d*sqrt(1/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(10*e^(4*I*d*x + 4*I*c) + 11*e^(2*I*d*x + 2*I*c) + 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
124,1,596,0,0.457260," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(3 i \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 3 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{\frac{1}{2}} {\left(-3 i \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + {\left(9 i \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 9 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + {\left(-9 i \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 9 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-28 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 13 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{12 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/12*(sqrt(1/2)*(3*I*a^2*d*e^(5*I*d*x + 5*I*c) - 3*I*a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(1/2)*(-3*I*a^2*d*e^(5*I*d*x + 5*I*c) + 3*I*a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + (9*I*a^2*d*e^(5*I*d*x + 5*I*c) - 9*I*a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + (-9*I*a^2*d*e^(5*I*d*x + 5*I*c) + 9*I*a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-28*I*e^(6*I*d*x + 6*I*c) - 13*I*e^(4*I*d*x + 4*I*c) + 16*I*e^(2*I*d*x + 2*I*c) + I))/(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))","B",0
125,1,678,0,0.470676," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 12 \, \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 69 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 69 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(37 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 33 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 50 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 21 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{48 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"-1/48*(12*sqrt(1/2)*(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 12*sqrt(1/2)*(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 69*(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 69*(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/(a^3*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(37*e^(8*I*d*x + 8*I*c) - 33*e^(6*I*d*x + 6*I*c) - 50*e^(4*I*d*x + 4*I*c) + 21*e^(2*I*d*x + 2*I*c) + 1))/(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))","B",0
126,1,342,0,0.462456," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 15 \, \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(983 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 1527 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 348 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 33 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)}}{120 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"-1/120*(15*sqrt(1/2)*(a^3*d*e^(7*I*d*x + 7*I*c) + a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/(a^5*d^2))*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 15*sqrt(1/2)*(a^3*d*e^(7*I*d*x + 7*I*c) + a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/(a^5*d^2))*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(983*e^(8*I*d*x + 8*I*c) + 1527*e^(6*I*d*x + 6*I*c) + 348*e^(4*I*d*x + 4*I*c) - 33*e^(2*I*d*x + 2*I*c) + 3))/(a^3*d*e^(7*I*d*x + 7*I*c) + a^3*d*e^(5*I*d*x + 5*I*c))","B",0
127,1,283,0,0.438626," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-15 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 15 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(463 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 194 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 26 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(-15*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 15*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(463*I*e^(6*I*d*x + 6*I*c) + 194*I*e^(4*I*d*x + 4*I*c) - 26*I*e^(2*I*d*x + 2*I*c) + 3*I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
128,1,283,0,0.445172," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(83 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 64 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 16 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(15*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 15*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(83*e^(6*I*d*x + 6*I*c) + 64*e^(4*I*d*x + 4*I*c) - 16*e^(2*I*d*x + 2*I*c) + 3))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
129,1,283,0,0.454272," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 5 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{3} d}"," ",0,"1/40*(5*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 5*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(6*I*d*x + 6*I*c) + 2*I*e^(4*I*d*x + 4*I*c) + 2*I*e^(2*I*d*x + 2*I*c) - I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
130,1,284,0,0.436844," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(17 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 16 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(15*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 15*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(17*e^(6*I*d*x + 6*I*c) + 16*e^(4*I*d*x + 4*I*c) - 4*e^(2*I*d*x + 2*I*c) - 3))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
131,1,283,0,0.449997," ","integrate(1/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-15 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 15 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(23 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 34 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 14 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(-15*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 15*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(23*I*e^(6*I*d*x + 6*I*c) + 34*I*e^(4*I*d*x + 4*I*c) + 14*I*e^(2*I*d*x + 2*I*c) + 3*I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
132,1,511,0,0.454809," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 5 \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 20 \, a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 20 \, a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(41 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 48 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{3} d}"," ",0,"1/40*(5*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 5*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 20*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 20*a^3*d*sqrt(1/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(41*e^(6*I*d*x + 6*I*c) + 48*e^(4*I*d*x + 4*I*c) + 8*e^(2*I*d*x + 2*I*c) + 1))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
133,1,610,0,0.469376," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(30 i \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - 30 i \, a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{\frac{1}{2}} {\left(-30 i \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + 30 i \, a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 2 \, {\left(150 i \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - 150 i \, a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, \sqrt{2} {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 2 \, {\left(-150 i \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + 150 i \, a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(16 \, {\left(3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, \sqrt{2} {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-403 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 151 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 280 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 31 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)}}{240 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"1/240*(sqrt(1/2)*(30*I*a^3*d*e^(7*I*d*x + 7*I*c) - 30*I*a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/(a^5*d^2))*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(1/2)*(-30*I*a^3*d*e^(7*I*d*x + 7*I*c) + 30*I*a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/(a^5*d^2))*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 2*(150*I*a^3*d*e^(7*I*d*x + 7*I*c) - 150*I*a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/(a^5*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) + 2*sqrt(2)*(a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 2*(-150*I*a^3*d*e^(7*I*d*x + 7*I*c) + 150*I*a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/(a^5*d^2))*log(16*(3*a^2*e^(2*I*d*x + 2*I*c) - 2*sqrt(2)*(a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a^2)*e^(-2*I*d*x - 2*I*c)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-403*I*e^(8*I*d*x + 8*I*c) - 151*I*e^(6*I*d*x + 6*I*c) + 280*I*e^(4*I*d*x + 4*I*c) + 31*I*e^(2*I*d*x + 2*I*c) + 3*I))/(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))","B",0
134,1,294,0,0.447270," ","integrate(1/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(-105 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 105 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(176 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 298 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 188 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 81 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 15 i\right)}\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{1680 \, a^{4} d}"," ",0,"1/1680*(-105*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(7*I*d*x + 7*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 105*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(7*I*d*x + 7*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(176*I*e^(8*I*d*x + 8*I*c) + 298*I*e^(6*I*d*x + 6*I*c) + 188*I*e^(4*I*d*x + 4*I*c) + 81*I*e^(2*I*d*x + 2*I*c) + 15*I))*e^(-7*I*d*x - 7*I*c)/(a^4*d)","B",0
135,1,371,0,0.453689," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-2 i \, a d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d^{2}}\right) - 15 \, \sqrt{\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-2 i \, a d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d^{2}}\right) - {\left(-184 i \, a d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 192 i \, a d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 104 i \, a d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/60*(15*sqrt(4*I*a^2*d^5/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((-2*I*a*d^3*e^(2*I*f*x + 2*I*e) + sqrt(4*I*a^2*d^5/f^2)*(I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*d^2)) - 15*sqrt(4*I*a^2*d^5/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((-2*I*a*d^3*e^(2*I*f*x + 2*I*e) + sqrt(4*I*a^2*d^5/f^2)*(-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*d^2)) - (-184*I*a*d^2*e^(4*I*f*x + 4*I*e) - 192*I*a*d^2*e^(2*I*f*x + 2*I*e) - 104*I*a*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
136,1,310,0,0.442484," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{-\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-2 i \, a d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{-\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d}\right) - 3 \, \sqrt{-\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-2 i \, a d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - \sqrt{-\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d}\right) - 16 \, {\left(2 \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + a d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/12*(3*sqrt(-4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((-2*I*a*d^2*e^(2*I*f*x + 2*I*e) + sqrt(-4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*d)) - 3*sqrt(-4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((-2*I*a*d^2*e^(2*I*f*x + 2*I*e) - sqrt(-4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*d)) - 16*(2*a*d*e^(2*I*f*x + 2*I*e) + a*d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
137,1,244,0,0.439801," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{\sqrt{\frac{4 i \, a^{2} d}{f^{2}}} f \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{4 i \, a^{2} d}{f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - \sqrt{\frac{4 i \, a^{2} d}{f^{2}}} f \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{4 i \, a^{2} d}{f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) + 8 i \, a \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, f}"," ",0,"1/4*(sqrt(4*I*a^2*d/f^2)*f*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(4*I*a^2*d/f^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a) - sqrt(4*I*a^2*d/f^2)*f*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(4*I*a^2*d/f^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a) + 8*I*a*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/f","B",0
138,1,212,0,0.431330," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{4 i \, a^{2}}{d f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - \frac{1}{4} \, \sqrt{-\frac{4 i \, a^{2}}{d f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right)"," ",0,"1/4*sqrt(-4*I*a^2/(d*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d*f^2)))*e^(-2*I*f*x - 2*I*e)/a) - 1/4*sqrt(-4*I*a^2/(d*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) - (d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d*f^2)))*e^(-2*I*f*x - 2*I*e)/a)","C",0
139,1,339,0,0.440905," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{\frac{4 i \, a^{2}}{d^{3} f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{d^{3} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{\frac{4 i \, a^{2}}{d^{3} f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{d^{3} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - {\left(-8 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)}}"," ",0,"-1/4*((d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(4*I*a^2/(d^3*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (I*d^2*f*e^(2*I*f*x + 2*I*e) + I*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/(d^3*f^2)))*e^(-2*I*f*x - 2*I*e)/a) - (d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(4*I*a^2/(d^3*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (-I*d^2*f*e^(2*I*f*x + 2*I*e) - I*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/(d^3*f^2)))*e^(-2*I*f*x - 2*I*e)/a) - (-8*I*a*e^(2*I*f*x + 2*I*e) - 8*I*a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)","C",0
140,1,390,0,0.454505," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{5} f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d^{5} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - 3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{5} f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d^{5} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - 16 \, {\left(2 \, a e^{\left(4 i \, f x + 4 i \, e\right)} + a e^{\left(2 i \, f x + 2 i \, e\right)} - a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)}}"," ",0,"-1/12*(3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(-4*I*a^2/(d^5*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d^5*f^2)))*e^(-2*I*f*x - 2*I*e)/a) - 3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(-4*I*a^2/(d^5*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) - (d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d^5*f^2)))*e^(-2*I*f*x - 2*I*e)/a) - 16*(2*a*e^(4*I*f*x + 4*I*e) + a*e^(2*I*f*x + 2*I*e) - a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)","B",0
141,1,453,0,0.459338," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{15 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{\frac{4 i \, a^{2}}{d^{7} f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{4} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{d^{7} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - 15 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{\frac{4 i \, a^{2}}{d^{7} f^{2}}} \log\left(\frac{{\left(-2 i \, a d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{4} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{d^{7} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) + {\left(184 i \, a e^{\left(6 i \, f x + 6 i \, e\right)} - 8 i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 88 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} + 104 i \, a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)}}"," ",0,"1/60*(15*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(4*I*a^2/(d^7*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (I*d^4*f*e^(2*I*f*x + 2*I*e) + I*d^4*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/(d^7*f^2)))*e^(-2*I*f*x - 2*I*e)/a) - 15*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(4*I*a^2/(d^7*f^2))*log((-2*I*a*d*e^(2*I*f*x + 2*I*e) + (-I*d^4*f*e^(2*I*f*x + 2*I*e) - I*d^4*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/(d^7*f^2)))*e^(-2*I*f*x - 2*I*e)/a) + (184*I*a*e^(6*I*f*x + 6*I*e) - 8*I*a*e^(4*I*f*x + 4*I*e) - 88*I*a*e^(2*I*f*x + 2*I*e) + 104*I*a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)","B",0
142,1,341,0,0.472649," ","integrate((d*tan(f*x+e))^(5/2)*(a-I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{15 \, \sqrt{-\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(2 \, a d^{3} + \sqrt{-\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{f}\right) - 15 \, \sqrt{-\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(2 \, a d^{3} - \sqrt{-\frac{4 i \, a^{2} d^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{f}\right) + {\left(104 i \, a d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 192 i \, a d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 184 i \, a d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/60*(15*sqrt(-4*I*a^2*d^5/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((2*a*d^3 + sqrt(-4*I*a^2*d^5/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/f) - 15*sqrt(-4*I*a^2*d^5/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((2*a*d^3 - sqrt(-4*I*a^2*d^5/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/f) + (104*I*a*d^2*e^(4*I*f*x + 4*I*e) + 192*I*a*d^2*e^(2*I*f*x + 2*I*e) + 184*I*a*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
143,1,286,0,0.447194," ","integrate((d*tan(f*x+e))^(3/2)*(a-I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-2 i \, a d^{2} + \sqrt{\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{f}\right) - 3 \, \sqrt{\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-2 i \, a d^{2} - \sqrt{\frac{4 i \, a^{2} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{f}\right) + 16 \, {\left(a d e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, a d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/12*(3*sqrt(4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((-2*I*a*d^2 + sqrt(4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/f) - 3*sqrt(4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((-2*I*a*d^2 - sqrt(4*I*a^2*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/f) + 16*(a*d*e^(2*I*f*x + 2*I*e) + 2*a*d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
144,1,223,0,0.432682," ","integrate((d*tan(f*x+e))^(1/2)*(a-I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{\sqrt{-\frac{4 i \, a^{2} d}{f^{2}}} f \log\left(-\frac{{\left(2 \, a d + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{4 i \, a^{2} d}{f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{f}\right) - \sqrt{-\frac{4 i \, a^{2} d}{f^{2}}} f \log\left(-\frac{{\left(2 \, a d - {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{4 i \, a^{2} d}{f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{f}\right) + 8 i \, a \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, f}"," ",0,"-1/4*(sqrt(-4*I*a^2*d/f^2)*f*log(-(2*a*d + (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-4*I*a^2*d/f^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/f) - sqrt(-4*I*a^2*d/f^2)*f*log(-(2*a*d - (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-4*I*a^2*d/f^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/f) + 8*I*a*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/f","B",0
145,1,169,0,0.422627," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{i \, a^{2}}{d f^{2}}} \log\left(\frac{d f \sqrt{\frac{i \, a^{2}}{d f^{2}}} + {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{a}\right) - \frac{1}{2} \, \sqrt{\frac{i \, a^{2}}{d f^{2}}} \log\left(-\frac{d f \sqrt{\frac{i \, a^{2}}{d f^{2}}} - {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{a}\right)"," ",0,"1/2*sqrt(I*a^2/(d*f^2))*log((d*f*sqrt(I*a^2/(d*f^2)) + (a*e^(2*I*f*x + 2*I*e) + a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/a) - 1/2*sqrt(I*a^2/(d*f^2))*log(-(d*f*sqrt(I*a^2/(d*f^2)) - (a*e^(2*I*f*x + 2*I*e) + a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/a)","C",0
146,1,313,0,0.502527," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{3} f^{2}}} \log\left(\frac{{\left({\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d^{3} f^{2}}} + 2 \, a\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d f}\right) - {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{3} f^{2}}} \log\left(-\frac{{\left({\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d^{3} f^{2}}} - 2 \, a\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d f}\right) + {\left(-8 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)}}"," ",0,"1/4*((d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(-4*I*a^2/(d^3*f^2))*log(((d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d^3*f^2)) + 2*a)*e^(-2*I*f*x - 2*I*e)/(d*f)) - (d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(-4*I*a^2/(d^3*f^2))*log(-((d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d^3*f^2)) - 2*a)*e^(-2*I*f*x - 2*I*e)/(d*f)) + (-8*I*a*e^(2*I*f*x + 2*I*e) - 8*I*a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)","C",0
147,1,376,0,0.585267," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{4 i \, a^{2}}{d^{5} f^{2}}} \log\left(-\frac{{\left({\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{d^{5} f^{2}}} + 2 i \, a\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2} f}\right) - 3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{4 i \, a^{2}}{d^{5} f^{2}}} \log\left(\frac{{\left({\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{d^{5} f^{2}}} - 2 i \, a\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2} f}\right) + 16 \, {\left(a e^{\left(4 i \, f x + 4 i \, e\right)} - a e^{\left(2 i \, f x + 2 i \, e\right)} - 2 \, a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)}}"," ",0,"-1/12*(3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(4*I*a^2/(d^5*f^2))*log(-((d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/(d^5*f^2)) + 2*I*a)*e^(-2*I*f*x - 2*I*e)/(d^2*f)) - 3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(4*I*a^2/(d^5*f^2))*log(((d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/(d^5*f^2)) - 2*I*a)*e^(-2*I*f*x - 2*I*e)/(d^2*f)) + 16*(a*e^(4*I*f*x + 4*I*e) - a*e^(2*I*f*x + 2*I*e) - 2*a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)","B",0
148,1,437,0,0.599006," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{7} f^{2}}} \log\left(-\frac{{\left({\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d^{7} f^{2}}} + 2 \, a\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3} f}\right) - 15 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{7} f^{2}}} \log\left(\frac{{\left({\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{d^{7} f^{2}}} - 2 \, a\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3} f}\right) - {\left(104 i \, a e^{\left(6 i \, f x + 6 i \, e\right)} - 88 i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 8 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} + 184 i \, a\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)}}"," ",0,"-1/60*(15*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(-4*I*a^2/(d^7*f^2))*log(-((d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d^7*f^2)) + 2*a)*e^(-2*I*f*x - 2*I*e)/(d^3*f)) - 15*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(-4*I*a^2/(d^7*f^2))*log(((d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/(d^7*f^2)) - 2*a)*e^(-2*I*f*x - 2*I*e)/(d^3*f)) - (104*I*a*e^(6*I*f*x + 6*I*e) - 88*I*a*e^(4*I*f*x + 4*I*e) - 8*I*a*e^(2*I*f*x + 2*I*e) + 184*I*a)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)","B",0
149,1,436,0,0.687169," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{16 i \, a^{4} d^{5}}{f^{2}}} {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-4 i \, a^{2} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{16 i \, a^{4} d^{5}}{f^{2}}} {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2} d^{2}}\right) - 105 \, \sqrt{\frac{16 i \, a^{4} d^{5}}{f^{2}}} {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-4 i \, a^{2} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{16 i \, a^{4} d^{5}}{f^{2}}} {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2} d^{2}}\right) - {\left(-2696 i \, a^{2} d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 4904 i \, a^{2} d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 4504 i \, a^{2} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 1336 i \, a^{2} d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{420 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/420*(105*sqrt(16*I*a^4*d^5/f^2)*(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)*log(1/2*(-4*I*a^2*d^3*e^(2*I*f*x + 2*I*e) + sqrt(16*I*a^4*d^5/f^2)*(I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*d^2)) - 105*sqrt(16*I*a^4*d^5/f^2)*(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)*log(1/2*(-4*I*a^2*d^3*e^(2*I*f*x + 2*I*e) + sqrt(16*I*a^4*d^5/f^2)*(-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*d^2)) - (-2696*I*a^2*d^2*e^(6*I*f*x + 6*I*e) - 4904*I*a^2*d^2*e^(4*I*f*x + 4*I*e) - 4504*I*a^2*d^2*e^(2*I*f*x + 2*I*e) - 1336*I*a^2*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
150,1,372,0,0.538618," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{15 \, \sqrt{-\frac{16 i \, a^{4} d^{3}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-4 i \, a^{2} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{-\frac{16 i \, a^{4} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2} d}\right) - 15 \, \sqrt{-\frac{16 i \, a^{4} d^{3}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-4 i \, a^{2} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - \sqrt{-\frac{16 i \, a^{4} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2} d}\right) - 8 \, {\left(43 \, a^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} + 54 \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + 23 \, a^{2} d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/60*(15*sqrt(-16*I*a^4*d^3/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log(1/2*(-4*I*a^2*d^2*e^(2*I*f*x + 2*I*e) + sqrt(-16*I*a^4*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*d)) - 15*sqrt(-16*I*a^4*d^3/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log(1/2*(-4*I*a^2*d^2*e^(2*I*f*x + 2*I*e) - sqrt(-16*I*a^4*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*d)) - 8*(43*a^2*d*e^(4*I*f*x + 4*I*e) + 54*a^2*d*e^(2*I*f*x + 2*I*e) + 23*a^2*d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
151,1,305,0,0.610948," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{16 i \, a^{4} d}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{16 i \, a^{4} d}{f^{2}}} {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 3 \, \sqrt{\frac{16 i \, a^{4} d}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{16 i \, a^{4} d}{f^{2}}} {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) + {\left(56 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 40 i \, a^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/12*(3*sqrt(16*I*a^4*d/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + sqrt(16*I*a^4*d/f^2)*(I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^2) - 3*sqrt(16*I*a^4*d/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + sqrt(16*I*a^4*d/f^2)*(-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^2) + (56*I*a^2*e^(2*I*f*x + 2*I*e) + 40*I*a^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
152,1,266,0,0.499340," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{d \sqrt{-\frac{16 i \, a^{4}}{d f^{2}}} f \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 i \, a^{4}}{d f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - d \sqrt{-\frac{16 i \, a^{4}}{d f^{2}}} f \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 i \, a^{4}}{d f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 8 \, a^{2} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, d f}"," ",0,"1/4*(d*sqrt(-16*I*a^4/(d*f^2))*f*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + (d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-16*I*a^4/(d*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^2) - d*sqrt(-16*I*a^4/(d*f^2))*f*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) - (d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-16*I*a^4/(d*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^2) - 8*a^2*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d*f)","C",0
153,1,349,0,0.637149," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{\frac{16 i \, a^{4}}{d^{3} f^{2}}} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{16 i \, a^{4}}{d^{3} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{\frac{16 i \, a^{4}}{d^{3} f^{2}}} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{16 i \, a^{4}}{d^{3} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - {\left(-8 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)}}"," ",0,"-1/4*((d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(16*I*a^4/(d^3*f^2))*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + (I*d^2*f*e^(2*I*f*x + 2*I*e) + I*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(16*I*a^4/(d^3*f^2)))*e^(-2*I*f*x - 2*I*e)/a^2) - (d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(16*I*a^4/(d^3*f^2))*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + (-I*d^2*f*e^(2*I*f*x + 2*I*e) - I*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(16*I*a^4/(d^3*f^2)))*e^(-2*I*f*x - 2*I*e)/a^2) - (-8*I*a^2*e^(2*I*f*x + 2*I*e) - 8*I*a^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)","C",0
154,1,403,0,0.583450," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{-\frac{16 i \, a^{4}}{d^{5} f^{2}}} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 i \, a^{4}}{d^{5} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{-\frac{16 i \, a^{4}}{d^{5} f^{2}}} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 i \, a^{4}}{d^{5} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 8 \, {\left(7 \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 5 \, a^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)}}"," ",0,"-1/12*(3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(-16*I*a^4/(d^5*f^2))*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + (d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-16*I*a^4/(d^5*f^2)))*e^(-2*I*f*x - 2*I*e)/a^2) - 3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(-16*I*a^4/(d^5*f^2))*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) - (d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-16*I*a^4/(d^5*f^2)))*e^(-2*I*f*x - 2*I*e)/a^2) - 8*(7*a^2*e^(4*I*f*x + 4*I*e) + 2*a^2*e^(2*I*f*x + 2*I*e) - 5*a^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)","B",0
155,1,467,0,0.582690," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{15 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{\frac{16 i \, a^{4}}{d^{7} f^{2}}} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{4} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{16 i \, a^{4}}{d^{7} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 15 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{\frac{16 i \, a^{4}}{d^{7} f^{2}}} \log\left(\frac{{\left(-4 i \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{4} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{16 i \, a^{4}}{d^{7} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) + {\left(344 i \, a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 88 i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 248 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 184 i \, a^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)}}"," ",0,"1/60*(15*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(16*I*a^4/(d^7*f^2))*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + (I*d^4*f*e^(2*I*f*x + 2*I*e) + I*d^4*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(16*I*a^4/(d^7*f^2)))*e^(-2*I*f*x - 2*I*e)/a^2) - 15*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(16*I*a^4/(d^7*f^2))*log(1/2*(-4*I*a^2*d*e^(2*I*f*x + 2*I*e) + (-I*d^4*f*e^(2*I*f*x + 2*I*e) - I*d^4*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(16*I*a^4/(d^7*f^2)))*e^(-2*I*f*x - 2*I*e)/a^2) + (344*I*a^2*e^(6*I*f*x + 6*I*e) - 88*I*a^2*e^(4*I*f*x + 4*I*e) - 248*I*a^2*e^(2*I*f*x + 2*I*e) + 184*I*a^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)","B",0
156,1,489,0,0.596908," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{315 \, \sqrt{\frac{64 i \, a^{6} d^{5}}{f^{2}}} {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{64 i \, a^{6} d^{5}}{f^{2}}} {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} d^{2}}\right) - 315 \, \sqrt{\frac{64 i \, a^{6} d^{5}}{f^{2}}} {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{64 i \, a^{6} d^{5}}{f^{2}}} {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} d^{2}}\right) - {\left(-16816 i \, a^{3} d^{2} e^{\left(8 i \, f x + 8 i \, e\right)} - 43760 i \, a^{3} d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 58128 i \, a^{3} d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 34640 i \, a^{3} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 7936 i \, a^{3} d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{1260 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/1260*(315*sqrt(64*I*a^6*d^5/f^2)*(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(-8*I*a^3*d^3*e^(2*I*f*x + 2*I*e) + sqrt(64*I*a^6*d^5/f^2)*(I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^3*d^2)) - 315*sqrt(64*I*a^6*d^5/f^2)*(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(-8*I*a^3*d^3*e^(2*I*f*x + 2*I*e) + sqrt(64*I*a^6*d^5/f^2)*(-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^3*d^2)) - (-16816*I*a^3*d^2*e^(8*I*f*x + 8*I*e) - 43760*I*a^3*d^2*e^(6*I*f*x + 6*I*e) - 58128*I*a^3*d^2*e^(4*I*f*x + 4*I*e) - 34640*I*a^3*d^2*e^(2*I*f*x + 2*I*e) - 7936*I*a^3*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
157,1,423,0,0.603707," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{105 \, \sqrt{-\frac{64 i \, a^{6} d^{3}}{f^{2}}} {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{-\frac{64 i \, a^{6} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} d}\right) - 105 \, \sqrt{-\frac{64 i \, a^{6} d^{3}}{f^{2}}} {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - \sqrt{-\frac{64 i \, a^{6} d^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} d}\right) - 16 \, {\left(319 \, a^{3} d e^{\left(6 i \, f x + 6 i \, e\right)} + 646 \, a^{3} d e^{\left(4 i \, f x + 4 i \, e\right)} + 551 \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + 164 \, a^{3} d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{420 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/420*(105*sqrt(-64*I*a^6*d^3/f^2)*(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(-8*I*a^3*d^2*e^(2*I*f*x + 2*I*e) + sqrt(-64*I*a^6*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^3*d)) - 105*sqrt(-64*I*a^6*d^3/f^2)*(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(-8*I*a^3*d^2*e^(2*I*f*x + 2*I*e) - sqrt(-64*I*a^6*d^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^3*d)) - 16*(319*a^3*d*e^(6*I*f*x + 6*I*e) + 646*a^3*d*e^(4*I*f*x + 4*I*e) + 551*a^3*d*e^(2*I*f*x + 2*I*e) + 164*a^3*d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
158,1,355,0,0.599255," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{5 \, \sqrt{\frac{64 i \, a^{6} d}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{64 i \, a^{6} d}{f^{2}}} {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 5 \, \sqrt{\frac{64 i \, a^{6} d}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{\frac{64 i \, a^{6} d}{f^{2}}} {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) + {\left(208 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 304 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 128 i \, a^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{20 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/20*(5*sqrt(64*I*a^6*d/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + sqrt(64*I*a^6*d/f^2)*(I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^3) - 5*sqrt(64*I*a^6*d/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + sqrt(64*I*a^6*d/f^2)*(-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^3) + (208*I*a^3*e^(4*I*f*x + 4*I*e) + 304*I*a^3*e^(2*I*f*x + 2*I*e) + 128*I*a^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
159,1,324,0,0.604689," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{-\frac{64 i \, a^{6}}{d f^{2}}} {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + \sqrt{-\frac{64 i \, a^{6}}{d f^{2}}} {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 3 \, \sqrt{-\frac{64 i \, a^{6}}{d f^{2}}} {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} - \sqrt{-\frac{64 i \, a^{6}}{d f^{2}}} {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 16 \, {\left(5 \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, a^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"1/12*(3*sqrt(-64*I*a^6/(d*f^2))*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + sqrt(-64*I*a^6/(d*f^2))*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^3) - 3*sqrt(-64*I*a^6/(d*f^2))*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) - sqrt(-64*I*a^6/(d*f^2))*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^3) - 16*(5*a^3*e^(2*I*f*x + 2*I*e) + 4*a^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
160,1,341,0,0.669072," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{-16 i \, a^{3} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{\frac{64 i \, a^{6}}{d^{3} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{2} f\right)} \sqrt{\frac{64 i \, a^{6}}{d^{3} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) + {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)} \sqrt{\frac{64 i \, a^{6}}{d^{3} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{2} f\right)} \sqrt{\frac{64 i \, a^{6}}{d^{3} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right)}{4 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{2} f\right)}}"," ",0,"1/4*(-16*I*a^3*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*e^(2*I*f*x + 2*I*e) - (d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(64*I*a^6/(d^3*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + (I*d^2*f*e^(2*I*f*x + 2*I*e) + I*d^2*f)*sqrt(64*I*a^6/(d^3*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^3) + (d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)*sqrt(64*I*a^6/(d^3*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + (-I*d^2*f*e^(2*I*f*x + 2*I*e) - I*d^2*f)*sqrt(64*I*a^6/(d^3*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/a^3))/(d^2*f*e^(2*I*f*x + 2*I*e) - d^2*f)","B",0
161,1,402,0,0.616104," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{-\frac{64 i \, a^{6}}{d^{5} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 i \, a^{6}}{d^{5} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 3 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{-\frac{64 i \, a^{6}}{d^{5} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 i \, a^{6}}{d^{5} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 16 \, {\left(5 \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 \, a^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} - 2 \, d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3} f\right)}}"," ",0,"-1/12*(3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(-64*I*a^6/(d^5*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + (d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-64*I*a^6/(d^5*f^2)))*e^(-2*I*f*x - 2*I*e)/a^3) - 3*(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt(-64*I*a^6/(d^5*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) - (d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-64*I*a^6/(d^5*f^2)))*e^(-2*I*f*x - 2*I*e)/a^3) - 16*(5*a^3*e^(4*I*f*x + 4*I*e) + a^3*e^(2*I*f*x + 2*I*e) - 4*a^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^3*f*e^(4*I*f*x + 4*I*e) - 2*d^3*f*e^(2*I*f*x + 2*I*e) + d^3*f)","B",0
162,1,467,0,0.587166," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{5 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{\frac{64 i \, a^{6}}{d^{7} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{4} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{64 i \, a^{6}}{d^{7} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 5 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)} \sqrt{\frac{64 i \, a^{6}}{d^{7} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{4} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{64 i \, a^{6}}{d^{7} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) + {\left(208 i \, a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 96 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 176 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 128 i \, a^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{20 \, {\left(d^{4} f e^{\left(6 i \, f x + 6 i \, e\right)} - 3 \, d^{4} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} - d^{4} f\right)}}"," ",0,"1/20*(5*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(64*I*a^6/(d^7*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + (I*d^4*f*e^(2*I*f*x + 2*I*e) + I*d^4*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(64*I*a^6/(d^7*f^2)))*e^(-2*I*f*x - 2*I*e)/a^3) - 5*(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)*sqrt(64*I*a^6/(d^7*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + (-I*d^4*f*e^(2*I*f*x + 2*I*e) - I*d^4*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(64*I*a^6/(d^7*f^2)))*e^(-2*I*f*x - 2*I*e)/a^3) + (208*I*a^3*e^(6*I*f*x + 6*I*e) - 96*I*a^3*e^(4*I*f*x + 4*I*e) - 176*I*a^3*e^(2*I*f*x + 2*I*e) + 128*I*a^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^4*f*e^(6*I*f*x + 6*I*e) - 3*d^4*f*e^(4*I*f*x + 4*I*e) + 3*d^4*f*e^(2*I*f*x + 2*I*e) - d^4*f)","B",0
163,1,521,0,0.711265," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{105 \, {\left(d^{5} f e^{\left(8 i \, f x + 8 i \, e\right)} - 4 \, d^{5} f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, d^{5} f e^{\left(4 i \, f x + 4 i \, e\right)} - 4 \, d^{5} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{5} f\right)} \sqrt{-\frac{64 i \, a^{6}}{d^{9} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(d^{5} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{5} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 i \, a^{6}}{d^{9} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 105 \, {\left(d^{5} f e^{\left(8 i \, f x + 8 i \, e\right)} - 4 \, d^{5} f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, d^{5} f e^{\left(4 i \, f x + 4 i \, e\right)} - 4 \, d^{5} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{5} f\right)} \sqrt{-\frac{64 i \, a^{6}}{d^{9} f^{2}}} \log\left(\frac{{\left(-8 i \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(d^{5} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{5} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 i \, a^{6}}{d^{9} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 16 \, {\left(319 \, a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} - 327 \, a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 95 \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 387 \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 164 \, a^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{420 \, {\left(d^{5} f e^{\left(8 i \, f x + 8 i \, e\right)} - 4 \, d^{5} f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, d^{5} f e^{\left(4 i \, f x + 4 i \, e\right)} - 4 \, d^{5} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{5} f\right)}}"," ",0,"1/420*(105*(d^5*f*e^(8*I*f*x + 8*I*e) - 4*d^5*f*e^(6*I*f*x + 6*I*e) + 6*d^5*f*e^(4*I*f*x + 4*I*e) - 4*d^5*f*e^(2*I*f*x + 2*I*e) + d^5*f)*sqrt(-64*I*a^6/(d^9*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) + (d^5*f*e^(2*I*f*x + 2*I*e) + d^5*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-64*I*a^6/(d^9*f^2)))*e^(-2*I*f*x - 2*I*e)/a^3) - 105*(d^5*f*e^(8*I*f*x + 8*I*e) - 4*d^5*f*e^(6*I*f*x + 6*I*e) + 6*d^5*f*e^(4*I*f*x + 4*I*e) - 4*d^5*f*e^(2*I*f*x + 2*I*e) + d^5*f)*sqrt(-64*I*a^6/(d^9*f^2))*log(1/4*(-8*I*a^3*d*e^(2*I*f*x + 2*I*e) - (d^5*f*e^(2*I*f*x + 2*I*e) + d^5*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-64*I*a^6/(d^9*f^2)))*e^(-2*I*f*x - 2*I*e)/a^3) - 16*(319*a^3*e^(8*I*f*x + 8*I*e) - 327*a^3*e^(6*I*f*x + 6*I*e) - 95*a^3*e^(4*I*f*x + 4*I*e) + 387*a^3*e^(2*I*f*x + 2*I*e) - 164*a^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^5*f*e^(8*I*f*x + 8*I*e) - 4*d^5*f*e^(6*I*f*x + 6*I*e) + 6*d^5*f*e^(4*I*f*x + 4*I*e) - 4*d^5*f*e^(2*I*f*x + 2*I*e) + d^5*f)","B",0
164,1,612,0,0.794451," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{9 i \, d^{7}}{a^{2} f^{2}}} {\left(a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(-3 i \, d^{4} + \sqrt{\frac{9 i \, d^{7}}{a^{2} f^{2}}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) - 3 \, \sqrt{\frac{9 i \, d^{7}}{a^{2} f^{2}}} {\left(a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(-3 i \, d^{4} - \sqrt{\frac{9 i \, d^{7}}{a^{2} f^{2}}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) + 3 \, \sqrt{-\frac{i \, d^{7}}{4 \, a^{2} f^{2}}} {\left(a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(-2 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, \sqrt{-\frac{i \, d^{7}}{4 \, a^{2} f^{2}}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3}}\right) - 3 \, \sqrt{-\frac{i \, d^{7}}{4 \, a^{2} f^{2}}} {\left(a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(-2 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 \, \sqrt{-\frac{i \, d^{7}}{4 \, a^{2} f^{2}}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3}}\right) + {\left(19 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 38 \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, d^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}\right)}}"," ",0,"1/12*(3*sqrt(9*I*d^7/(a^2*f^2))*(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))*log((-3*I*d^4 + sqrt(9*I*d^7/(a^2*f^2))*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)) - 3*sqrt(9*I*d^7/(a^2*f^2))*(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))*log((-3*I*d^4 - sqrt(9*I*d^7/(a^2*f^2))*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)) + 3*sqrt(-1/4*I*d^7/(a^2*f^2))*(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))*log((-2*I*d^4*e^(2*I*f*x + 2*I*e) + 4*sqrt(-1/4*I*d^7/(a^2*f^2))*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^3) - 3*sqrt(-1/4*I*d^7/(a^2*f^2))*(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))*log((-2*I*d^4*e^(2*I*f*x + 2*I*e) - 4*sqrt(-1/4*I*d^7/(a^2*f^2))*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^3) + (19*d^3*e^(4*I*f*x + 4*I*e) + 38*d^3*e^(2*I*f*x + 2*I*e) + 3*d^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))","B",0
165,1,533,0,0.590088," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a \sqrt{\frac{i \, d^{5}}{4 \, a^{2} f^{2}}} f e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a f\right)} \sqrt{\frac{i \, d^{5}}{4 \, a^{2} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2}}\right) - a \sqrt{\frac{i \, d^{5}}{4 \, a^{2} f^{2}}} f e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a f\right)} \sqrt{\frac{i \, d^{5}}{4 \, a^{2} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2}}\right) + a \sqrt{-\frac{4 i \, d^{5}}{a^{2} f^{2}}} f e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(2 \, d^{3} + {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{4 i \, d^{5}}{a^{2} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) - a \sqrt{-\frac{4 i \, d^{5}}{a^{2} f^{2}}} f e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(2 \, d^{3} - {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{4 i \, d^{5}}{a^{2} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) - {\left(-9 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"-1/4*(a*sqrt(1/4*I*d^5/(a^2*f^2))*f*e^(2*I*f*x + 2*I*e)*log((-2*I*d^3*e^(2*I*f*x + 2*I*e) + (4*I*a*f*e^(2*I*f*x + 2*I*e) + 4*I*a*f)*sqrt(1/4*I*d^5/(a^2*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^2) - a*sqrt(1/4*I*d^5/(a^2*f^2))*f*e^(2*I*f*x + 2*I*e)*log((-2*I*d^3*e^(2*I*f*x + 2*I*e) + (-4*I*a*f*e^(2*I*f*x + 2*I*e) - 4*I*a*f)*sqrt(1/4*I*d^5/(a^2*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^2) + a*sqrt(-4*I*d^5/(a^2*f^2))*f*e^(2*I*f*x + 2*I*e)*log(-(2*d^3 + (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-4*I*d^5/(a^2*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)) - a*sqrt(-4*I*d^5/(a^2*f^2))*f*e^(2*I*f*x + 2*I*e)*log(-(2*d^3 - (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-4*I*d^5/(a^2*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)) - (-9*I*d^2*e^(2*I*f*x + 2*I*e) - I*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
166,1,521,0,0.699351," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a f \sqrt{-\frac{i \, d^{3}}{4 \, a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{3}}{4 \, a^{2} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d}\right) - a f \sqrt{-\frac{i \, d^{3}}{4 \, a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{3}}{4 \, a^{2} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d}\right) - a f \sqrt{\frac{i \, d^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, d^{2} + {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{3}}{a^{2} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) + a f \sqrt{\frac{i \, d^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, d^{2} - {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{3}}{a^{2} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) + {\left(d e^{\left(2 i \, f x + 2 i \, e\right)} + d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"-1/4*(a*f*sqrt(-1/4*I*d^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((-2*I*d^2*e^(2*I*f*x + 2*I*e) + 4*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I*d^3/(a^2*f^2)))*e^(-2*I*f*x - 2*I*e)/d) - a*f*sqrt(-1/4*I*d^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((-2*I*d^2*e^(2*I*f*x + 2*I*e) - 4*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I*d^3/(a^2*f^2)))*e^(-2*I*f*x - 2*I*e)/d) - a*f*sqrt(I*d^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((I*d^2 + (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I*d^3/(a^2*f^2)))*e^(-2*I*f*x - 2*I*e)/(a*f)) + a*f*sqrt(I*d^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((I*d^2 - (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I*d^3/(a^2*f^2)))*e^(-2*I*f*x - 2*I*e)/(a*f)) + (d*e^(2*I*f*x + 2*I*e) + d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
167,1,283,0,0.623687," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a f \sqrt{\frac{i \, d}{4 \, a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left({\left({\left(4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d}{4 \, a^{2} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - a f \sqrt{\frac{i \, d}{4 \, a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left({\left({\left(-4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d}{4 \, a^{2} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*(a*f*sqrt(1/4*I*d/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(((4*I*a*f*e^(2*I*f*x + 2*I*e) + 4*I*a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/4*I*d/(a^2*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - a*f*sqrt(1/4*I*d/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(((-4*I*a*f*e^(2*I*f*x + 2*I*e) - 4*I*a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/4*I*d/(a^2*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(I*e^(2*I*f*x + 2*I*e) + I))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
168,1,514,0,0.713008," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a d f \sqrt{-\frac{i}{4 \, a^{2} d f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-{\left(4 \, {\left(a d f e^{\left(2 i \, f x + 2 i \, e\right)} + a d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{4 \, a^{2} d f^{2}}} + 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - a d f \sqrt{-\frac{i}{4 \, a^{2} d f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left({\left(4 \, {\left(a d f e^{\left(2 i \, f x + 2 i \, e\right)} + a d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{4 \, a^{2} d f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - a d f \sqrt{\frac{i}{a^{2} d f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left({\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{a^{2} d f^{2}}} + i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) + a d f \sqrt{\frac{i}{a^{2} d f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left({\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{a^{2} d f^{2}}} - i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a d f}"," ",0,"-1/4*(a*d*f*sqrt(-1/4*I/(a^2*d*f^2))*e^(2*I*f*x + 2*I*e)*log(-(4*(a*d*f*e^(2*I*f*x + 2*I*e) + a*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I/(a^2*d*f^2)) + 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - a*d*f*sqrt(-1/4*I/(a^2*d*f^2))*e^(2*I*f*x + 2*I*e)*log((4*(a*d*f*e^(2*I*f*x + 2*I*e) + a*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I/(a^2*d*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - a*d*f*sqrt(I/(a^2*d*f^2))*e^(2*I*f*x + 2*I*e)*log(((a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/(a^2*d*f^2)) + I)*e^(-2*I*f*x - 2*I*e)/(a*f)) + a*d*f*sqrt(I/(a^2*d*f^2))*e^(2*I*f*x + 2*I*e)*log(-((a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/(a^2*d*f^2)) - I)*e^(-2*I*f*x - 2*I*e)/(a*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-2*I*f*x - 2*I*e)/(a*d*f)","B",0
169,1,642,0,0.674596," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{i}{4 \, a^{2} d^{3} f^{2}}} \log\left({\left({\left(4 i \, a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{4 \, a^{2} d^{3} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left(a d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{i}{4 \, a^{2} d^{3} f^{2}}} \log\left({\left({\left(-4 i \, a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{4 \, a^{2} d^{3} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left(a d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{-\frac{4 i}{a^{2} d^{3} f^{2}}} \log\left(\frac{{\left({\left(a d f e^{\left(2 i \, f x + 2 i \, e\right)} + a d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i}{a^{2} d^{3} f^{2}}} + 2\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d f}\right) + {\left(a d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{-\frac{4 i}{a^{2} d^{3} f^{2}}} \log\left(-\frac{{\left({\left(a d f e^{\left(2 i \, f x + 2 i \, e\right)} + a d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i}{a^{2} d^{3} f^{2}}} - 2\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-9 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 8 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}}{4 \, {\left(a d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} - a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)}}"," ",0,"-1/4*((a*d^2*f*e^(4*I*f*x + 4*I*e) - a*d^2*f*e^(2*I*f*x + 2*I*e))*sqrt(1/4*I/(a^2*d^3*f^2))*log(((4*I*a*d^2*f*e^(2*I*f*x + 2*I*e) + 4*I*a*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/4*I/(a^2*d^3*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - (a*d^2*f*e^(4*I*f*x + 4*I*e) - a*d^2*f*e^(2*I*f*x + 2*I*e))*sqrt(1/4*I/(a^2*d^3*f^2))*log(((-4*I*a*d^2*f*e^(2*I*f*x + 2*I*e) - 4*I*a*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/4*I/(a^2*d^3*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - (a*d^2*f*e^(4*I*f*x + 4*I*e) - a*d^2*f*e^(2*I*f*x + 2*I*e))*sqrt(-4*I/(a^2*d^3*f^2))*log(((a*d*f*e^(2*I*f*x + 2*I*e) + a*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I/(a^2*d^3*f^2)) + 2)*e^(-2*I*f*x - 2*I*e)/(a*d*f)) + (a*d^2*f*e^(4*I*f*x + 4*I*e) - a*d^2*f*e^(2*I*f*x + 2*I*e))*sqrt(-4*I/(a^2*d^3*f^2))*log(-((a*d*f*e^(2*I*f*x + 2*I*e) + a*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I/(a^2*d^3*f^2)) - 2)*e^(-2*I*f*x - 2*I*e)/(a*d*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(-9*I*e^(4*I*f*x + 4*I*e) - 8*I*e^(2*I*f*x + 2*I*e) + I))/(a*d^2*f*e^(4*I*f*x + 4*I*e) - a*d^2*f*e^(2*I*f*x + 2*I*e))","B",0
170,1,737,0,0.655133," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 \, {\left(a d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} - 2 \, a d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} + a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{-\frac{i}{4 \, a^{2} d^{5} f^{2}}} \log\left(-{\left(4 \, {\left(a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{4 \, a^{2} d^{5} f^{2}}} + 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 3 \, {\left(a d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} - 2 \, a d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} + a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{-\frac{i}{4 \, a^{2} d^{5} f^{2}}} \log\left({\left(4 \, {\left(a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{4 \, a^{2} d^{5} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 3 \, {\left(a d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} - 2 \, a d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} + a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{9 i}{a^{2} d^{5} f^{2}}} \log\left(-\frac{{\left({\left(a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{9 i}{a^{2} d^{5} f^{2}}} + 3 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d^{2} f}\right) + 3 \, {\left(a d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} - 2 \, a d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} + a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{9 i}{a^{2} d^{5} f^{2}}} \log\left(\frac{{\left({\left(a d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{9 i}{a^{2} d^{5} f^{2}}} - 3 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a d^{2} f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(19 \, e^{\left(6 i \, f x + 6 i \, e\right)} - 19 \, e^{\left(4 i \, f x + 4 i \, e\right)} - 35 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3\right)}}{12 \, {\left(a d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} - 2 \, a d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} + a d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)}}"," ",0,"1/12*(3*(a*d^3*f*e^(6*I*f*x + 6*I*e) - 2*a*d^3*f*e^(4*I*f*x + 4*I*e) + a*d^3*f*e^(2*I*f*x + 2*I*e))*sqrt(-1/4*I/(a^2*d^5*f^2))*log(-(4*(a*d^3*f*e^(2*I*f*x + 2*I*e) + a*d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I/(a^2*d^5*f^2)) + 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 3*(a*d^3*f*e^(6*I*f*x + 6*I*e) - 2*a*d^3*f*e^(4*I*f*x + 4*I*e) + a*d^3*f*e^(2*I*f*x + 2*I*e))*sqrt(-1/4*I/(a^2*d^5*f^2))*log((4*(a*d^3*f*e^(2*I*f*x + 2*I*e) + a*d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I/(a^2*d^5*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 3*(a*d^3*f*e^(6*I*f*x + 6*I*e) - 2*a*d^3*f*e^(4*I*f*x + 4*I*e) + a*d^3*f*e^(2*I*f*x + 2*I*e))*sqrt(9*I/(a^2*d^5*f^2))*log(-((a*d^2*f*e^(2*I*f*x + 2*I*e) + a*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(9*I/(a^2*d^5*f^2)) + 3*I)*e^(-2*I*f*x - 2*I*e)/(a*d^2*f)) + 3*(a*d^3*f*e^(6*I*f*x + 6*I*e) - 2*a*d^3*f*e^(4*I*f*x + 4*I*e) + a*d^3*f*e^(2*I*f*x + 2*I*e))*sqrt(9*I/(a^2*d^5*f^2))*log(((a*d^2*f*e^(2*I*f*x + 2*I*e) + a*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(9*I/(a^2*d^5*f^2)) - 3*I)*e^(-2*I*f*x - 2*I*e)/(a*d^2*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(19*e^(6*I*f*x + 6*I*e) - 19*e^(4*I*f*x + 4*I*e) - 35*e^(2*I*f*x + 2*I*e) + 3))/(a*d^3*f*e^(6*I*f*x + 6*I*e) - 2*a*d^3*f*e^(4*I*f*x + 4*I*e) + a*d^3*f*e^(2*I*f*x + 2*I*e))","B",0
171,1,668,0,0.538229," ","integrate((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(a^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{2209 i \, d^{9}}{64 \, a^{4} f^{2}}} \log\left(-\frac{{\left(47 \, d^{5} + 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{-\frac{2209 i \, d^{9}}{64 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - 12 \, {\left(a^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{2209 i \, d^{9}}{64 \, a^{4} f^{2}}} \log\left(-\frac{{\left(47 \, d^{5} - 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{-\frac{2209 i \, d^{9}}{64 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - 12 \, {\left(a^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{i \, d^{9}}{16 \, a^{4} f^{2}}} \log\left(\frac{{\left(-2 i \, d^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} f\right)} \sqrt{\frac{i \, d^{9}}{16 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{4}}\right) + 12 \, {\left(a^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{i \, d^{9}}{16 \, a^{4} f^{2}}} \log\left(\frac{{\left(-2 i \, d^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2} f\right)} \sqrt{\frac{i \, d^{9}}{16 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{4}}\right) - {\left(-202 i \, d^{4} e^{\left(6 i \, f x + 6 i \, e\right)} - 305 i \, d^{4} e^{\left(4 i \, f x + 4 i \, e\right)} - 36 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, d^{4}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{48 \, {\left(a^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)}}"," ",0,"-1/48*(12*(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*sqrt(-2209/64*I*d^9/(a^4*f^2))*log(-1/8*(47*d^5 + 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-2209/64*I*d^9/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - 12*(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*sqrt(-2209/64*I*d^9/(a^4*f^2))*log(-1/8*(47*d^5 - 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-2209/64*I*d^9/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - 12*(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*sqrt(1/16*I*d^9/(a^4*f^2))*log((-2*I*d^5*e^(2*I*f*x + 2*I*e) + (8*I*a^2*f*e^(2*I*f*x + 2*I*e) + 8*I*a^2*f)*sqrt(1/16*I*d^9/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^4) + 12*(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))*sqrt(1/16*I*d^9/(a^4*f^2))*log((-2*I*d^5*e^(2*I*f*x + 2*I*e) + (-8*I*a^2*f*e^(2*I*f*x + 2*I*e) - 8*I*a^2*f)*sqrt(1/16*I*d^9/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^4) - (-202*I*d^4*e^(6*I*f*x + 6*I*e) - 305*I*d^4*e^(4*I*f*x + 4*I*e) - 36*I*d^4*e^(2*I*f*x + 2*I*e) + 3*I*d^4)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))","B",0
172,1,572,0,0.575605," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} \sqrt{-\frac{i \, d^{7}}{16 \, a^{4} f^{2}}} f e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{-\frac{i \, d^{7}}{16 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3}}\right) - 4 \, a^{2} \sqrt{-\frac{i \, d^{7}}{16 \, a^{4} f^{2}}} f e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{-\frac{i \, d^{7}}{16 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3}}\right) + 4 \, a^{2} \sqrt{\frac{529 i \, d^{7}}{64 \, a^{4} f^{2}}} f e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(23 i \, d^{4} + 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{529 i \, d^{7}}{64 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - 4 \, a^{2} \sqrt{\frac{529 i \, d^{7}}{64 \, a^{4} f^{2}}} f e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(23 i \, d^{4} - 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{529 i \, d^{7}}{64 \, a^{4} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - {\left(42 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 9 \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - d^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"1/16*(4*a^2*sqrt(-1/16*I*d^7/(a^4*f^2))*f*e^(4*I*f*x + 4*I*e)*log((-2*I*d^4*e^(2*I*f*x + 2*I*e) + 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-1/16*I*d^7/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^3) - 4*a^2*sqrt(-1/16*I*d^7/(a^4*f^2))*f*e^(4*I*f*x + 4*I*e)*log((-2*I*d^4*e^(2*I*f*x + 2*I*e) - 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(-1/16*I*d^7/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^3) + 4*a^2*sqrt(529/64*I*d^7/(a^4*f^2))*f*e^(4*I*f*x + 4*I*e)*log(1/8*(23*I*d^4 + 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(529/64*I*d^7/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - 4*a^2*sqrt(529/64*I*d^7/(a^4*f^2))*f*e^(4*I*f*x + 4*I*e)*log(1/8*(23*I*d^4 - 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(529/64*I*d^7/(a^4*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - (42*d^3*e^(4*I*f*x + 4*I*e) + 9*d^3*e^(2*I*f*x + 2*I*e) - d^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
173,1,574,0,0.661262," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{2} f \sqrt{\frac{i \, d^{5}}{16 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{5}}{16 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2}}\right) - 4 \, a^{2} f \sqrt{\frac{i \, d^{5}}{16 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{5}}{16 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2}}\right) - 4 \, a^{2} f \sqrt{-\frac{49 i \, d^{5}}{64 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(7 \, d^{3} + 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{49 i \, d^{5}}{64 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) + 4 \, a^{2} f \sqrt{-\frac{49 i \, d^{5}}{64 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(7 \, d^{3} - 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{49 i \, d^{5}}{64 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - {\left(6 i \, d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 5 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"-1/16*(4*a^2*f*sqrt(1/16*I*d^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log((-2*I*d^3*e^(2*I*f*x + 2*I*e) + (8*I*a^2*f*e^(2*I*f*x + 2*I*e) + 8*I*a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I*d^5/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/d^2) - 4*a^2*f*sqrt(1/16*I*d^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log((-2*I*d^3*e^(2*I*f*x + 2*I*e) + (-8*I*a^2*f*e^(2*I*f*x + 2*I*e) - 8*I*a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I*d^5/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/d^2) - 4*a^2*f*sqrt(-49/64*I*d^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(7*d^3 + 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-49/64*I*d^5/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) + 4*a^2*f*sqrt(-49/64*I*d^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(7*d^3 - 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-49/64*I*d^5/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - (6*I*d^2*e^(4*I*f*x + 4*I*e) + 5*I*d^2*e^(2*I*f*x + 2*I*e) - I*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
174,1,565,0,0.591301," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{2} f \sqrt{-\frac{i \, d^{3}}{16 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{3}}{16 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d}\right) - 4 \, a^{2} f \sqrt{-\frac{i \, d^{3}}{16 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{3}}{16 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d}\right) - 4 \, a^{2} f \sqrt{\frac{i \, d^{3}}{64 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(i \, d^{2} + 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{3}}{64 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) + 4 \, a^{2} f \sqrt{\frac{i \, d^{3}}{64 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(i \, d^{2} - 8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{3}}{64 \, a^{4} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - {\left(2 \, d e^{\left(4 i \, f x + 4 i \, e\right)} + d e^{\left(2 i \, f x + 2 i \, e\right)} - d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"-1/16*(4*a^2*f*sqrt(-1/16*I*d^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log((-2*I*d^2*e^(2*I*f*x + 2*I*e) + 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/16*I*d^3/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/d) - 4*a^2*f*sqrt(-1/16*I*d^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log((-2*I*d^2*e^(2*I*f*x + 2*I*e) - 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/16*I*d^3/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/d) - 4*a^2*f*sqrt(1/64*I*d^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(I*d^2 + 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I*d^3/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) + 4*a^2*f*sqrt(1/64*I*d^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(I*d^2 - 8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I*d^3/(a^4*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - (2*d*e^(4*I*f*x + 4*I*e) + d*e^(2*I*f*x + 2*I*e) - d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
175,1,531,0,0.543689," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} f \sqrt{\frac{i \, d}{16 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left({\left({\left(8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d}{16 \, a^{4} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, a^{2} f \sqrt{\frac{i \, d}{16 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left({\left({\left(-8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d}{16 \, a^{4} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 4 \, a^{2} f \sqrt{-\frac{i \, d}{64 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d}{64 \, a^{4} f^{2}}} + d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - 4 \, a^{2} f \sqrt{-\frac{i \, d}{64 \, a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d}{64 \, a^{4} f^{2}}} - d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) + \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(2 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"1/16*(4*a^2*f*sqrt(1/16*I*d/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(((8*I*a^2*f*e^(2*I*f*x + 2*I*e) + 8*I*a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I*d/(a^4*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 4*a^2*f*sqrt(1/16*I*d/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(((-8*I*a^2*f*e^(2*I*f*x + 2*I*e) - 8*I*a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I*d/(a^4*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + 4*a^2*f*sqrt(-1/64*I*d/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d/(a^4*f^2)) + d)*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - 4*a^2*f*sqrt(-1/64*I*d/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d/(a^4*f^2)) - d)*e^(-2*I*f*x - 2*I*e)/(a^2*f)) + sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(2*I*e^(4*I*f*x + 4*I*e) + 3*I*e^(2*I*f*x + 2*I*e) + I))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
176,1,556,0,0.731088," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{2} d f \sqrt{-\frac{i}{16 \, a^{4} d f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-{\left(8 \, {\left(a^{2} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{16 \, a^{4} d f^{2}}} + 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, a^{2} d f \sqrt{-\frac{i}{16 \, a^{4} d f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left({\left(8 \, {\left(a^{2} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{16 \, a^{4} d f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, a^{2} d f \sqrt{\frac{49 i}{64 \, a^{4} d f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{49 i}{64 \, a^{4} d f^{2}}} + 7 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) + 4 \, a^{2} d f \sqrt{\frac{49 i}{64 \, a^{4} d f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{49 i}{64 \, a^{4} d f^{2}}} - 7 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(6 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 7 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} d f}"," ",0,"-1/16*(4*a^2*d*f*sqrt(-1/16*I/(a^4*d*f^2))*e^(4*I*f*x + 4*I*e)*log(-(8*(a^2*d*f*e^(2*I*f*x + 2*I*e) + a^2*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/16*I/(a^4*d*f^2)) + 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 4*a^2*d*f*sqrt(-1/16*I/(a^4*d*f^2))*e^(4*I*f*x + 4*I*e)*log((8*(a^2*d*f*e^(2*I*f*x + 2*I*e) + a^2*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/16*I/(a^4*d*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 4*a^2*d*f*sqrt(49/64*I/(a^4*d*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(49/64*I/(a^4*d*f^2)) + 7*I)*e^(-2*I*f*x - 2*I*e)/(a^2*f)) + 4*a^2*d*f*sqrt(49/64*I/(a^4*d*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(8*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(49/64*I/(a^4*d*f^2)) - 7*I)*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(6*e^(4*I*f*x + 4*I*e) + 7*e^(2*I*f*x + 2*I*e) + 1))*e^(-4*I*f*x - 4*I*e)/(a^2*d*f)","B",0
177,1,694,0,0.557390," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{2} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{i}{16 \, a^{4} d^{3} f^{2}}} \log\left({\left({\left(8 i \, a^{2} d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{16 \, a^{4} d^{3} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, {\left(a^{2} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{i}{16 \, a^{4} d^{3} f^{2}}} \log\left({\left({\left(-8 i \, a^{2} d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2} d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{16 \, a^{4} d^{3} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, {\left(a^{2} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{529 i}{64 \, a^{4} d^{3} f^{2}}} \log\left(\frac{{\left(8 \, {\left(a^{2} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{529 i}{64 \, a^{4} d^{3} f^{2}}} + 23\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} d f}\right) + 4 \, {\left(a^{2} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{529 i}{64 \, a^{4} d^{3} f^{2}}} \log\left(-\frac{{\left(8 \, {\left(a^{2} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{529 i}{64 \, a^{4} d^{3} f^{2}}} - 23\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} d f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-42 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 33 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 10 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}}{16 \, {\left(a^{2} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)}}"," ",0,"-1/16*(4*(a^2*d^2*f*e^(6*I*f*x + 6*I*e) - a^2*d^2*f*e^(4*I*f*x + 4*I*e))*sqrt(1/16*I/(a^4*d^3*f^2))*log(((8*I*a^2*d^2*f*e^(2*I*f*x + 2*I*e) + 8*I*a^2*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I/(a^4*d^3*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 4*(a^2*d^2*f*e^(6*I*f*x + 6*I*e) - a^2*d^2*f*e^(4*I*f*x + 4*I*e))*sqrt(1/16*I/(a^4*d^3*f^2))*log(((-8*I*a^2*d^2*f*e^(2*I*f*x + 2*I*e) - 8*I*a^2*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I/(a^4*d^3*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 4*(a^2*d^2*f*e^(6*I*f*x + 6*I*e) - a^2*d^2*f*e^(4*I*f*x + 4*I*e))*sqrt(-529/64*I/(a^4*d^3*f^2))*log(1/8*(8*(a^2*d*f*e^(2*I*f*x + 2*I*e) + a^2*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-529/64*I/(a^4*d^3*f^2)) + 23)*e^(-2*I*f*x - 2*I*e)/(a^2*d*f)) + 4*(a^2*d^2*f*e^(6*I*f*x + 6*I*e) - a^2*d^2*f*e^(4*I*f*x + 4*I*e))*sqrt(-529/64*I/(a^4*d^3*f^2))*log(-1/8*(8*(a^2*d*f*e^(2*I*f*x + 2*I*e) + a^2*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-529/64*I/(a^4*d^3*f^2)) - 23)*e^(-2*I*f*x - 2*I*e)/(a^2*d*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(-42*I*e^(6*I*f*x + 6*I*e) - 33*I*e^(4*I*f*x + 4*I*e) + 10*I*e^(2*I*f*x + 2*I*e) + I))/(a^2*d^2*f*e^(6*I*f*x + 6*I*e) - a^2*d^2*f*e^(4*I*f*x + 4*I*e))","B",0
178,1,797,0,0.636432," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{12 \, {\left(a^{2} d^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} - 2 \, a^{2} d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{i}{16 \, a^{4} d^{5} f^{2}}} \log\left(-{\left(8 \, {\left(a^{2} d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{5} f^{2}}} + 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, {\left(a^{2} d^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} - 2 \, a^{2} d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{i}{16 \, a^{4} d^{5} f^{2}}} \log\left({\left(8 \, {\left(a^{2} d^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{5} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, {\left(a^{2} d^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} - 2 \, a^{2} d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{2209 i}{64 \, a^{4} d^{5} f^{2}}} \log\left(-\frac{{\left(8 \, {\left(a^{2} d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{2209 i}{64 \, a^{4} d^{5} f^{2}}} + 47 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} d^{2} f}\right) + 12 \, {\left(a^{2} d^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} - 2 \, a^{2} d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{2209 i}{64 \, a^{4} d^{5} f^{2}}} \log\left(\frac{{\left(8 \, {\left(a^{2} d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{2209 i}{64 \, a^{4} d^{5} f^{2}}} - 47 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} d^{2} f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(202 \, e^{\left(8 i \, f x + 8 i \, e\right)} - 103 \, e^{\left(6 i \, f x + 6 i \, e\right)} - 269 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 39 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3\right)}}{48 \, {\left(a^{2} d^{3} f e^{\left(8 i \, f x + 8 i \, e\right)} - 2 \, a^{2} d^{3} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} d^{3} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)}}"," ",0,"1/48*(12*(a^2*d^3*f*e^(8*I*f*x + 8*I*e) - 2*a^2*d^3*f*e^(6*I*f*x + 6*I*e) + a^2*d^3*f*e^(4*I*f*x + 4*I*e))*sqrt(-1/16*I/(a^4*d^5*f^2))*log(-(8*(a^2*d^3*f*e^(2*I*f*x + 2*I*e) + a^2*d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/16*I/(a^4*d^5*f^2)) + 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*(a^2*d^3*f*e^(8*I*f*x + 8*I*e) - 2*a^2*d^3*f*e^(6*I*f*x + 6*I*e) + a^2*d^3*f*e^(4*I*f*x + 4*I*e))*sqrt(-1/16*I/(a^4*d^5*f^2))*log((8*(a^2*d^3*f*e^(2*I*f*x + 2*I*e) + a^2*d^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/16*I/(a^4*d^5*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*(a^2*d^3*f*e^(8*I*f*x + 8*I*e) - 2*a^2*d^3*f*e^(6*I*f*x + 6*I*e) + a^2*d^3*f*e^(4*I*f*x + 4*I*e))*sqrt(2209/64*I/(a^4*d^5*f^2))*log(-1/8*(8*(a^2*d^2*f*e^(2*I*f*x + 2*I*e) + a^2*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(2209/64*I/(a^4*d^5*f^2)) + 47*I)*e^(-2*I*f*x - 2*I*e)/(a^2*d^2*f)) + 12*(a^2*d^3*f*e^(8*I*f*x + 8*I*e) - 2*a^2*d^3*f*e^(6*I*f*x + 6*I*e) + a^2*d^3*f*e^(4*I*f*x + 4*I*e))*sqrt(2209/64*I/(a^4*d^5*f^2))*log(1/8*(8*(a^2*d^2*f*e^(2*I*f*x + 2*I*e) + a^2*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(2209/64*I/(a^4*d^5*f^2)) - 47*I)*e^(-2*I*f*x - 2*I*e)/(a^2*d^2*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(202*e^(8*I*f*x + 8*I*e) - 103*e^(6*I*f*x + 6*I*e) - 269*e^(4*I*f*x + 4*I*e) + 39*e^(2*I*f*x + 2*I*e) + 3))/(a^2*d^3*f*e^(8*I*f*x + 8*I*e) - 2*a^2*d^3*f*e^(6*I*f*x + 6*I*e) + a^2*d^3*f*e^(4*I*f*x + 4*I*e))","B",0
179,1,587,0,0.550587," ","integrate((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, a^{3} \sqrt{\frac{i \, d^{9}}{64 \, a^{6} f^{2}}} f e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} f\right)} \sqrt{\frac{i \, d^{9}}{64 \, a^{6} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{4}}\right) - 12 \, a^{3} \sqrt{\frac{i \, d^{9}}{64 \, a^{6} f^{2}}} f e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, a^{3} f\right)} \sqrt{\frac{i \, d^{9}}{64 \, a^{6} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{4}}\right) + 12 \, a^{3} \sqrt{-\frac{841 i \, d^{9}}{64 \, a^{6} f^{2}}} f e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(29 \, d^{5} + 8 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{-\frac{841 i \, d^{9}}{64 \, a^{6} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} f}\right) - 12 \, a^{3} \sqrt{-\frac{841 i \, d^{9}}{64 \, a^{6} f^{2}}} f e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(29 \, d^{5} - 8 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{-\frac{841 i \, d^{9}}{64 \, a^{6} f^{2}}} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} f}\right) + {\left(146 i \, d^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 41 i \, d^{4} e^{\left(4 i \, f x + 4 i \, e\right)} - 8 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d^{4}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} f}"," ",0,"1/48*(12*a^3*sqrt(1/64*I*d^9/(a^6*f^2))*f*e^(6*I*f*x + 6*I*e)*log((-2*I*d^5*e^(2*I*f*x + 2*I*e) + (16*I*a^3*f*e^(2*I*f*x + 2*I*e) + 16*I*a^3*f)*sqrt(1/64*I*d^9/(a^6*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^4) - 12*a^3*sqrt(1/64*I*d^9/(a^6*f^2))*f*e^(6*I*f*x + 6*I*e)*log((-2*I*d^5*e^(2*I*f*x + 2*I*e) + (-16*I*a^3*f*e^(2*I*f*x + 2*I*e) - 16*I*a^3*f)*sqrt(1/64*I*d^9/(a^6*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/d^4) + 12*a^3*sqrt(-841/64*I*d^9/(a^6*f^2))*f*e^(6*I*f*x + 6*I*e)*log(1/8*(29*d^5 + 8*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(-841/64*I*d^9/(a^6*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^3*f)) - 12*a^3*sqrt(-841/64*I*d^9/(a^6*f^2))*f*e^(6*I*f*x + 6*I*e)*log(1/8*(29*d^5 - 8*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(-841/64*I*d^9/(a^6*f^2))*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a^3*f)) + (146*I*d^4*e^(6*I*f*x + 6*I*e) + 41*I*d^4*e^(4*I*f*x + 4*I*e) - 8*I*d^4*e^(2*I*f*x + 2*I*e) + I*d^4)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
180,1,583,0,0.624497," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, a^{3} f \sqrt{-\frac{i \, d^{7}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{7}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3}}\right) - 12 \, a^{3} f \sqrt{-\frac{i \, d^{7}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - 16 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{7}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{3}}\right) + 12 \, a^{3} f \sqrt{\frac{9 i \, d^{7}}{16 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-3 i \, d^{4} + 4 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{9 i \, d^{7}}{16 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} f}\right) - 12 \, a^{3} f \sqrt{\frac{9 i \, d^{7}}{16 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-3 i \, d^{4} - 4 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{9 i \, d^{7}}{16 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} f}\right) + {\left(20 \, d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 14 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 5 \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + d^{3}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} f}"," ",0,"1/48*(12*a^3*f*sqrt(-1/64*I*d^7/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((-2*I*d^4*e^(2*I*f*x + 2*I*e) + 16*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d^7/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/d^3) - 12*a^3*f*sqrt(-1/64*I*d^7/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((-2*I*d^4*e^(2*I*f*x + 2*I*e) - 16*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d^7/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/d^3) + 12*a^3*f*sqrt(9/16*I*d^7/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4*(-3*I*d^4 + 4*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(9/16*I*d^7/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^3*f)) - 12*a^3*f*sqrt(9/16*I*d^7/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4*(-3*I*d^4 - 4*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(9/16*I*d^7/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^3*f)) + (20*d^3*e^(6*I*f*x + 6*I*e) + 14*d^3*e^(4*I*f*x + 4*I*e) - 5*d^3*e^(2*I*f*x + 2*I*e) + d^3)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
181,1,584,0,0.529846," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, a^{3} f \sqrt{\frac{i \, d^{5}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{5}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2}}\right) - 12 \, a^{3} f \sqrt{\frac{i \, d^{5}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d^{5}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d^{2}}\right) - 12 \, a^{3} f \sqrt{-\frac{i \, d^{5}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(d^{3} + 8 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{5}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} f}\right) + 12 \, a^{3} f \sqrt{-\frac{i \, d^{5}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(d^{3} - 8 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{5}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} f}\right) - {\left(-2 i \, d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + i \, d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - i \, d^{2}\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} f}"," ",0,"-1/48*(12*a^3*f*sqrt(1/64*I*d^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((-2*I*d^3*e^(2*I*f*x + 2*I*e) + (16*I*a^3*f*e^(2*I*f*x + 2*I*e) + 16*I*a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I*d^5/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/d^2) - 12*a^3*f*sqrt(1/64*I*d^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((-2*I*d^3*e^(2*I*f*x + 2*I*e) + (-16*I*a^3*f*e^(2*I*f*x + 2*I*e) - 16*I*a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I*d^5/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/d^2) - 12*a^3*f*sqrt(-1/64*I*d^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(d^3 + 8*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d^5/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^3*f)) + 12*a^3*f*sqrt(-1/64*I*d^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(d^3 - 8*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d^5/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/(a^3*f)) - (-2*I*d^2*e^(6*I*f*x + 6*I*e) + I*d^2*e^(4*I*f*x + 4*I*e) + 2*I*d^2*e^(2*I*f*x + 2*I*e) - I*d^2)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
182,1,340,0,0.610216," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, a^{3} f \sqrt{-\frac{i \, d^{3}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{3}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d}\right) - 12 \, a^{3} f \sqrt{-\frac{i \, d^{3}}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(-2 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 16 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d^{3}}{64 \, a^{6} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{d}\right) - {\left(4 \, d e^{\left(6 i \, f x + 6 i \, e\right)} + 4 \, d e^{\left(4 i \, f x + 4 i \, e\right)} - d e^{\left(2 i \, f x + 2 i \, e\right)} - d\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} f}"," ",0,"-1/48*(12*a^3*f*sqrt(-1/64*I*d^3/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((-2*I*d^2*e^(2*I*f*x + 2*I*e) + 16*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d^3/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/d) - 12*a^3*f*sqrt(-1/64*I*d^3/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((-2*I*d^2*e^(2*I*f*x + 2*I*e) - 16*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d^3/(a^6*f^2)))*e^(-2*I*f*x - 2*I*e)/d) - (4*d*e^(6*I*f*x + 6*I*e) + 4*d*e^(4*I*f*x + 4*I*e) - d*e^(2*I*f*x + 2*I*e) - d)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
183,1,542,0,0.688112," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, a^{3} f \sqrt{\frac{i \, d}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left({\left({\left(16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d}{64 \, a^{6} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, a^{3} f \sqrt{\frac{i \, d}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left({\left({\left(-16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, d}{64 \, a^{6} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 12 \, a^{3} f \sqrt{-\frac{i \, d}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(8 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d}{64 \, a^{6} f^{2}}} + d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} f}\right) - 12 \, a^{3} f \sqrt{-\frac{i \, d}{64 \, a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(8 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, d}{64 \, a^{6} f^{2}}} - d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} f}\right) + \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(2 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 5 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 4 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} f}"," ",0,"1/48*(12*a^3*f*sqrt(1/64*I*d/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(((16*I*a^3*f*e^(2*I*f*x + 2*I*e) + 16*I*a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I*d/(a^6*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*a^3*f*sqrt(1/64*I*d/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(((-16*I*a^3*f*e^(2*I*f*x + 2*I*e) - 16*I*a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I*d/(a^6*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + 12*a^3*f*sqrt(-1/64*I*d/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(8*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d/(a^6*f^2)) + d)*e^(-2*I*f*x - 2*I*e)/(a^3*f)) - 12*a^3*f*sqrt(-1/64*I*d/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/8*(8*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I*d/(a^6*f^2)) - d)*e^(-2*I*f*x - 2*I*e)/(a^3*f)) + sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(2*I*e^(6*I*f*x + 6*I*e) + 5*I*e^(4*I*f*x + 4*I*e) + 4*I*e^(2*I*f*x + 2*I*e) + I))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
184,1,568,0,0.591659," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, a^{3} d f \sqrt{-\frac{i}{64 \, a^{6} d f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-2 \, {\left(8 \, {\left(a^{3} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{64 \, a^{6} d f^{2}}} + i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, a^{3} d f \sqrt{-\frac{i}{64 \, a^{6} d f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(2 \, {\left(8 \, {\left(a^{3} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{64 \, a^{6} d f^{2}}} - i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, a^{3} d f \sqrt{\frac{9 i}{16 \, a^{6} d f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(4 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{9 i}{16 \, a^{6} d f^{2}}} + 3 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} f}\right) + 12 \, a^{3} d f \sqrt{\frac{9 i}{16 \, a^{6} d f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(4 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{9 i}{16 \, a^{6} d f^{2}}} - 3 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3} f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(20 \, e^{\left(6 i \, f x + 6 i \, e\right)} + 26 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 7 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} d f}"," ",0,"-1/48*(12*a^3*d*f*sqrt(-1/64*I/(a^6*d*f^2))*e^(6*I*f*x + 6*I*e)*log(-2*(8*(a^3*d*f*e^(2*I*f*x + 2*I*e) + a^3*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I/(a^6*d*f^2)) + I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*a^3*d*f*sqrt(-1/64*I/(a^6*d*f^2))*e^(6*I*f*x + 6*I*e)*log(2*(8*(a^3*d*f*e^(2*I*f*x + 2*I*e) + a^3*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/64*I/(a^6*d*f^2)) - I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*a^3*d*f*sqrt(9/16*I/(a^6*d*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4*(4*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(9/16*I/(a^6*d*f^2)) + 3*I)*e^(-2*I*f*x - 2*I*e)/(a^3*f)) + 12*a^3*d*f*sqrt(9/16*I/(a^6*d*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/4*(4*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(9/16*I/(a^6*d*f^2)) - 3*I)*e^(-2*I*f*x - 2*I*e)/(a^3*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(20*e^(6*I*f*x + 6*I*e) + 26*e^(4*I*f*x + 4*I*e) + 7*e^(2*I*f*x + 2*I*e) + 1))*e^(-6*I*f*x - 6*I*e)/(a^3*d*f)","B",0
185,1,705,0,0.588992," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(a^{3} d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} - a^{3} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{i}{64 \, a^{6} d^{3} f^{2}}} \log\left({\left({\left(16 i \, a^{3} d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{64 \, a^{6} d^{3} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, {\left(a^{3} d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} - a^{3} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{i}{64 \, a^{6} d^{3} f^{2}}} \log\left({\left({\left(-16 i \, a^{3} d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, a^{3} d^{2} f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{64 \, a^{6} d^{3} f^{2}}} - 2 i \, d e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 12 \, {\left(a^{3} d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} - a^{3} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{-\frac{841 i}{64 \, a^{6} d^{3} f^{2}}} \log\left(\frac{{\left(8 \, {\left(a^{3} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{841 i}{64 \, a^{6} d^{3} f^{2}}} + 29\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} d f}\right) + 12 \, {\left(a^{3} d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} - a^{3} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{-\frac{841 i}{64 \, a^{6} d^{3} f^{2}}} \log\left(-\frac{{\left(8 \, {\left(a^{3} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} d f\right)} \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{841 i}{64 \, a^{6} d^{3} f^{2}}} - 29\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{3} d f}\right) - \sqrt{\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-146 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 105 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 49 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 9 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}}{48 \, {\left(a^{3} d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} - a^{3} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)}}"," ",0,"-1/48*(12*(a^3*d^2*f*e^(8*I*f*x + 8*I*e) - a^3*d^2*f*e^(6*I*f*x + 6*I*e))*sqrt(1/64*I/(a^6*d^3*f^2))*log(((16*I*a^3*d^2*f*e^(2*I*f*x + 2*I*e) + 16*I*a^3*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I/(a^6*d^3*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*(a^3*d^2*f*e^(8*I*f*x + 8*I*e) - a^3*d^2*f*e^(6*I*f*x + 6*I*e))*sqrt(1/64*I/(a^6*d^3*f^2))*log(((-16*I*a^3*d^2*f*e^(2*I*f*x + 2*I*e) - 16*I*a^3*d^2*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I/(a^6*d^3*f^2)) - 2*I*d*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 12*(a^3*d^2*f*e^(8*I*f*x + 8*I*e) - a^3*d^2*f*e^(6*I*f*x + 6*I*e))*sqrt(-841/64*I/(a^6*d^3*f^2))*log(1/8*(8*(a^3*d*f*e^(2*I*f*x + 2*I*e) + a^3*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-841/64*I/(a^6*d^3*f^2)) + 29)*e^(-2*I*f*x - 2*I*e)/(a^3*d*f)) + 12*(a^3*d^2*f*e^(8*I*f*x + 8*I*e) - a^3*d^2*f*e^(6*I*f*x + 6*I*e))*sqrt(-841/64*I/(a^6*d^3*f^2))*log(-1/8*(8*(a^3*d*f*e^(2*I*f*x + 2*I*e) + a^3*d*f)*sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-841/64*I/(a^6*d^3*f^2)) - 29)*e^(-2*I*f*x - 2*I*e)/(a^3*d*f)) - sqrt((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(-146*I*e^(8*I*f*x + 8*I*e) - 105*I*e^(6*I*f*x + 6*I*e) + 49*I*e^(4*I*f*x + 4*I*e) + 9*I*e^(2*I*f*x + 2*I*e) + I))/(a^3*d^2*f*e^(8*I*f*x + 8*I*e) - a^3*d^2*f*e^(6*I*f*x + 6*I*e))","B",0
186,1,559,0,0.649012," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + i \, e^{\left(i \, d x + i \, c\right)}\right)} + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{49 i \, a}{16 \, d^{2}}} \log\left(\frac{1}{7} \, {\left(7 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + 8 i \, d \sqrt{\frac{49 i \, a}{16 \, d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{49 i \, a}{16 \, d^{2}}} \log\left(\frac{1}{7} \, {\left(7 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - 8 i \, d \sqrt{\frac{49 i \, a}{16 \, d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(3*I*d*x + 3*I*c) + I*e^(I*d*x + I*c)) + 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(49/16*I*a/d^2)*log(1/7*(7*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + 8*I*d*sqrt(49/16*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(49/16*I*a/d^2)*log(1/7*(7*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - 8*I*d*sqrt(49/16*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
187,1,479,0,0.641665," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} + d \sqrt{-\frac{i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + 2 \, d \sqrt{-\frac{i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - d \sqrt{-\frac{i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - 2 \, d \sqrt{-\frac{i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - d \sqrt{-\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + d \sqrt{-\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + d \sqrt{-\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - d \sqrt{-\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{2 \, d}"," ",0,"1/2*(2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) + d*sqrt(-I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + 2*d*sqrt(-I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - d*sqrt(-I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - 2*d*sqrt(-I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - d*sqrt(-2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + d*sqrt(-2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + d*sqrt(-2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - d*sqrt(-2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/d","B",0
188,1,413,0,0.607800," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{4 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + i \, d \sqrt{\frac{4 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \frac{1}{2} \, \sqrt{\frac{4 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - i \, d \sqrt{\frac{4 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \frac{1}{2} \, \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \frac{1}{2} \, \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)"," ",0,"-1/2*sqrt(4*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + I*d*sqrt(4*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 1/2*sqrt(4*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - I*d*sqrt(4*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 1/2*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 1/2*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c))","B",0
189,1,206,0,0.483532," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + d \sqrt{-\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \frac{1}{2} \, \sqrt{-\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - d \sqrt{-\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)"," ",0,"1/2*sqrt(-2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + d*sqrt(-2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 1/2*sqrt(-2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - d*sqrt(-2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c))","B",0
190,1,328,0,0.492424," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-4 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, e^{\left(i \, d x + i \, c\right)}\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/2*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-4*I*e^(3*I*d*x + 3*I*c) - 4*I*e^(I*d*x + I*c)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
191,1,355,0,0.582271," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(5 i \, d x + 5 i \, c\right)} + e^{\left(3 i \, d x + 3 i \, c\right)}\right)} - 3 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + d \sqrt{-\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - d \sqrt{-\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{6 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6*(8*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(5*I*d*x + 5*I*c) + e^(3*I*d*x + 3*I*c)) - 3*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + d*sqrt(-2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - d*sqrt(-2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
192,1,423,0,0.550938," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(68 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 12 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 20 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 60 i \, e^{\left(i \, d x + i \, c\right)}\right)} + 15 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 15 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{2 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} - i \, d \sqrt{\frac{2 i \, a}{d^{2}}} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{30 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/30*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(68*I*e^(7*I*d*x + 7*I*c) - 12*I*e^(5*I*d*x + 5*I*c) - 20*I*e^(3*I*d*x + 3*I*c) + 60*I*e^(I*d*x + I*c)) + 15*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) + I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 15*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*sqrt(2*I*a/d^2)*log((sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1) - I*d*sqrt(2*I*a/d^2)*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
193,1,673,0,0.702968," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-49 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} - 38 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 21 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{529 i \, a^{3}}{64 \, d^{2}}} \log\left(\frac{{\left(23 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 16 i \, \sqrt{\frac{529 i \, a^{3}}{64 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{23 \, a}\right) - 12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{529 i \, a^{3}}{64 \, d^{2}}} \log\left(\frac{{\left(23 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 16 i \, \sqrt{\frac{529 i \, a^{3}}{64 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{23 \, a}\right) - 12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + 12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{24 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/24*(sqrt(2)*(-49*I*a*e^(5*I*d*x + 5*I*c) - 38*I*a*e^(3*I*d*x + 3*I*c) - 21*I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 12*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(529/64*I*a^3/d^2)*log(1/23*(23*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 16*I*sqrt(529/64*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 12*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(529/64*I*a^3/d^2)*log(1/23*(23*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 16*I*sqrt(529/64*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 12*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 12*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
194,1,600,0,0.649560," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(7 \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{121 i \, a^{3}}{16 \, d^{2}}} \log\left(\frac{{\left(11 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 8 \, \sqrt{-\frac{121 i \, a^{3}}{16 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{11 \, a}\right) - 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{121 i \, a^{3}}{16 \, d^{2}}} \log\left(\frac{{\left(11 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 8 \, \sqrt{-\frac{121 i \, a^{3}}{16 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{11 \, a}\right) - 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*(7*a*e^(3*I*d*x + 3*I*c) + 3*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-121/16*I*a^3/d^2)*log(1/11*(11*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 8*sqrt(-121/16*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-121/16*I*a^3/d^2)*log(1/11*(11*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 8*sqrt(-121/16*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 2*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
195,1,525,0,0.617617," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} a \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} - \sqrt{\frac{9 i \, a^{3}}{d^{2}}} d \log\left(\frac{{\left(3 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 2 i \, \sqrt{\frac{9 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{3 \, a}\right) + \sqrt{\frac{9 i \, a^{3}}{d^{2}}} d \log\left(\frac{{\left(3 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 2 i \, \sqrt{\frac{9 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{3 \, a}\right) + \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) - \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{2 \, d}"," ",0,"1/2*(2*I*sqrt(2)*a*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) - sqrt(9*I*a^3/d^2)*d*log(1/3*(3*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 2*I*sqrt(9*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + sqrt(9*I*a^3/d^2)*d*log(1/3*(3*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 2*I*sqrt(9*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + sqrt(8*I*a^3/d^2)*d*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - sqrt(8*I*a^3/d^2)*d*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/d","B",0
196,1,451,0,0.526775," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) - \frac{1}{2} \, \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) - \frac{1}{2} \, \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right)"," ",0,"1/2*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 1/2*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 1/2*sqrt(-4*I*a^3/d^2)*log((sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-4*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 1/2*sqrt(-4*I*a^3/d^2)*log((sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-4*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a)","B",0
197,1,352,0,0.483887," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/2*(sqrt(2)*(-4*I*a*e^(3*I*d*x + 3*I*c) - 4*I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + (d*e^(2*I*d*x + 2*I*c) - d)*sqrt(8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
198,1,395,0,0.640218," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(5 \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 3 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + 3 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{6 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6*(4*sqrt(2)*(5*a*e^(5*I*d*x + 5*I*c) + 2*a*e^(3*I*d*x + 3*I*c) - 3*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 3*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 3*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
199,1,449,0,0.587813," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(36 i \, a e^{\left(7 i \, d x + 7 i \, c\right)} - 4 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} - 20 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 20 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 5 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) - 5 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{10 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/10*(sqrt(2)*(36*I*a*e^(7*I*d*x + 7*I*c) - 4*I*a*e^(5*I*d*x + 5*I*c) - 20*I*a*e^(3*I*d*x + 3*I*c) + 20*I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 5*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*sqrt(8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 5*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*sqrt(8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
200,1,491,0,0.476870," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(211 \, a e^{\left(9 i \, d x + 9 i \, c\right)} - 160 \, a e^{\left(7 i \, d x + 7 i \, c\right)} + 14 \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 280 \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 105 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 105 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + 105 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{8 i \, a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{210 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/210*(4*sqrt(2)*(211*a*e^(9*I*d*x + 9*I*c) - 160*a*e^(7*I*d*x + 7*I*c) + 14*a*e^(5*I*d*x + 5*I*c) + 280*a*e^(3*I*d*x + 3*I*c) - 105*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 105*(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 105*(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a^3/d^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-8*I*a^3/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
201,1,769,0,0.825511," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-845 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 1275 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 1135 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 321 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 96 \, \sqrt{\frac{131769 i \, a^{5}}{4096 \, d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(363 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 128 i \, \sqrt{\frac{131769 i \, a^{5}}{4096 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{363 \, a^{2}}\right) - 96 \, \sqrt{\frac{131769 i \, a^{5}}{4096 \, d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(363 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 128 i \, \sqrt{\frac{131769 i \, a^{5}}{4096 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{363 \, a^{2}}\right) - 96 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 96 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{192 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/192*(sqrt(2)*(-845*I*a^2*e^(7*I*d*x + 7*I*c) - 1275*I*a^2*e^(5*I*d*x + 5*I*c) - 1135*I*a^2*e^(3*I*d*x + 3*I*c) - 321*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 96*sqrt(131769/4096*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/363*(363*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 128*I*sqrt(131769/4096*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - 96*sqrt(131769/4096*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/363*(363*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 128*I*sqrt(131769/4096*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - 96*sqrt(32*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 96*sqrt(32*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
202,1,694,0,0.605040," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(91 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 98 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 39 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 12 \, \sqrt{-\frac{2025 i \, a^{5}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(45 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 16 \, \sqrt{-\frac{2025 i \, a^{5}}{64 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{45 \, a^{2}}\right) - 12 \, \sqrt{-\frac{2025 i \, a^{5}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(45 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 16 \, \sqrt{-\frac{2025 i \, a^{5}}{64 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{45 \, a^{2}}\right) - 12 \, \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 12 \, \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{24 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/24*(sqrt(2)*(91*a^2*e^(5*I*d*x + 5*I*c) + 98*a^2*e^(3*I*d*x + 3*I*c) + 39*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 12*sqrt(-2025/64*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/45*(45*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 16*sqrt(-2025/64*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - 12*sqrt(-2025/64*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/45*(45*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 16*sqrt(-2025/64*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - 12*sqrt(-32*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 12*sqrt(-32*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
203,1,621,0,0.651003," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(11 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 7 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 2 \, \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(23 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 8 i \, \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{23 \, a^{2}}\right) + 2 \, \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(23 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 8 i \, \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{23 \, a^{2}}\right) + 2 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) - 2 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*(11*I*a^2*e^(3*I*d*x + 3*I*c) + 7*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 2*sqrt(529/16*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/23*(23*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 8*I*sqrt(529/16*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 2*sqrt(529/16*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/23*(23*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 8*I*sqrt(529/16*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 2*sqrt(32*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - 2*sqrt(32*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
204,1,542,0,0.700498," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} a^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} d \log\left(\frac{{\left(5 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 2 \, \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{5 \, a^{2}}\right) - \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} d \log\left(\frac{{\left(5 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 2 \, \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{5 \, a^{2}}\right) - \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{2 \, d}"," ",0,"-1/2*(2*sqrt(2)*a^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c) + sqrt(-25*I*a^5/d^2)*d*log(1/5*(5*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 2*sqrt(-25*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - sqrt(-25*I*a^5/d^2)*d*log(1/5*(5*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 2*sqrt(-25*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - sqrt(-32*I*a^5/d^2)*d*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + sqrt(-32*I*a^5/d^2)*d*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/d","B",0
205,1,625,0,0.517225," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + \sqrt{\frac{4 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(\sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{4 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - \sqrt{\frac{4 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(\sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{4 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/2*(sqrt(2)*(-4*I*a^2*e^(3*I*d*x + 3*I*c) - 4*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(32*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + sqrt(32*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + sqrt(4*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(4*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - sqrt(4*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log((sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(4*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
206,1,408,0,0.527827," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(4 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 3 \, \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 3 \, \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{6 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6*(8*sqrt(2)*(4*a^2*e^(5*I*d*x + 5*I*c) + a^2*e^(3*I*d*x + 3*I*c) - 3*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 3*sqrt(-32*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 3*sqrt(-32*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
207,1,465,0,0.561425," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(208 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 72 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 160 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 120 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 15 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) - 15 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{30 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/30*(sqrt(2)*(208*I*a^2*e^(7*I*d*x + 7*I*c) - 72*I*a^2*e^(5*I*d*x + 5*I*c) - 160*I*a^2*e^(3*I*d*x + 3*I*c) + 120*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + 15*sqrt(32*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) - 15*sqrt(32*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
208,1,509,0,0.733983," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(40 \, a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} - 37 \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 7 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 49 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 21 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 21 \, \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 21 \, \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - \sqrt{-\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{42 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/42*(8*sqrt(2)*(40*a^2*e^(9*I*d*x + 9*I*c) - 37*a^2*e^(7*I*d*x + 7*I*c) - 7*a^2*e^(5*I*d*x + 5*I*c) + 49*a^2*e^(3*I*d*x + 3*I*c) - 21*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 21*sqrt(-32*I*a^5/d^2)*(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 21*sqrt(-32*I*a^5/d^2)*(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(-32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(8*I*d*x + 8*I*c) - 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) - 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
209,1,565,0,0.585802," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-5168 i \, a^{2} e^{\left(11 i \, d x + 11 i \, c\right)} + 8008 i \, a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} - 5472 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 7728 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 8400 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 2520 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - 315 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 315 \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, \sqrt{\frac{32 i \, a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{630 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} - 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} - 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/630*(sqrt(2)*(-5168*I*a^2*e^(11*I*d*x + 11*I*c) + 8008*I*a^2*e^(9*I*d*x + 9*I*c) - 5472*I*a^2*e^(7*I*d*x + 7*I*c) - 7728*I*a^2*e^(5*I*d*x + 5*I*c) + 8400*I*a^2*e^(3*I*d*x + 3*I*c) - 2520*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - 315*sqrt(32*I*a^5/d^2)*(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) + I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2) + 315*sqrt(32*I*a^5/d^2)*(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)) - I*sqrt(32*I*a^5/d^2)*d*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a^2))/(d*e^(10*I*d*x + 10*I*c) - 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) - 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) - d)","B",0
210,1,658,0,0.733937," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2\right)} + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{2 i}{a d^{2}}} \log\left(\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{2 i}{a d^{2}}} \log\left(-\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{121 i}{16 \, a d^{2}}} \log\left(\frac{208 \, {\left(11 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + 2 \, {\left(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{-\frac{121 i}{16 \, a d^{2}}}\right)}}{6655 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{121 i}{16 \, a d^{2}}} \log\left(\frac{208 \, {\left(11 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} - 2 \, {\left(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{-\frac{121 i}{16 \, a d^{2}}}\right)}}{6655 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right)}{4 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/4*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(3*e^(4*I*d*x + 4*I*c) + 9*e^(2*I*d*x + 2*I*c) + 2) + (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-2*I/(a*d^2))*log(1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-2*I/(a*d^2))*log(-1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-121/16*I/(a*d^2))*log(208/6655*(11*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + 2*(3*a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(-121/16*I/(a*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-121/16*I/(a*d^2))*log(208/6655*(11*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) - 2*(3*a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(-121/16*I/(a*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)))/(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
211,1,578,0,0.845521," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + a d \sqrt{\frac{i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{208 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(312 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 104 i \, a d\right)} \sqrt{\frac{i}{a d^{2}}}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) - a d \sqrt{\frac{i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{208 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(-312 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 104 i \, a d\right)} \sqrt{\frac{i}{a d^{2}}}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(-1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + a*d*sqrt(I/(a*d^2))*e^(I*d*x + I*c)*log(1/605*(208*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (312*I*a*d*e^(2*I*d*x + 2*I*c) - 104*I*a*d)*sqrt(I/(a*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) - a*d*sqrt(I/(a*d^2))*e^(I*d*x + I*c)*log(1/605*(208*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (-312*I*a*d*e^(2*I*d*x + 2*I*c) + 104*I*a*d)*sqrt(I/(a*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-6*I*e^(2*I*d*x + 2*I*c) - 2*I))*e^(-I*d*x - I*c)/(a*d)","B",0
212,1,577,0,0.730090," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - a d \sqrt{-\frac{4 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{-\frac{4 i}{a d^{2}}}\right)}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + a d \sqrt{-\frac{4 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} - {\left(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{-\frac{4 i}{a d^{2}}}\right)}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log(1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log(-1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - a*d*sqrt(-4*I/(a*d^2))*e^(I*d*x + I*c)*log(52/605*(4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (3*a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(-4*I/(a*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + a*d*sqrt(-4*I/(a*d^2))*e^(I*d*x + I*c)*log(52/605*(4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) - (3*a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(-4*I/(a*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1))*e^(-I*d*x - I*c)/(a*d)","B",0
213,1,300,0,0.554560," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(-1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(2*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-I*d*x - I*c)/(a*d)","B",0
214,1,299,0,0.606156," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log(1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log(-1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1))*e^(-I*d*x - I*c)/(a*d)","B",0
215,1,354,0,0.617491," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-10 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} - {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{2 i}{a d^{2}}} \log\left(\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{2 i}{a d^{2}}} \log\left(-\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{4 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/4*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-10*I*e^(4*I*d*x + 4*I*c) - 8*I*e^(2*I*d*x + 2*I*c) + 2*I) - (a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(2*I/(a*d^2))*log(1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + (a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(2*I/(a*d^2))*log(-1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))","B",0
216,1,403,0,0.521512," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(7 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 11 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 15 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)} + 3 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{2 i}{a d^{2}}} \log\left(\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{2 i}{a d^{2}}} \log\left(-\frac{1}{4} \, a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{12 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"-1/12*(2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(7*e^(6*I*d*x + 6*I*c) - 11*e^(4*I*d*x + 4*I*c) - 15*e^(2*I*d*x + 2*I*c) + 3) + 3*(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-2*I/(a*d^2))*log(1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(-2*I/(a*d^2))*log(-1/4*a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
217,1,455,0,0.732702," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(206 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 204 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 80 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 300 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 30 i\right)} + 15 \, {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} - 3 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{2 i}{a d^{2}}} \log\left(\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 15 \, {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} - 3 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{2 i}{a d^{2}}} \log\left(-\frac{1}{4} i \, a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{60 \, {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} - 3 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/60*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(206*I*e^(8*I*d*x + 8*I*c) - 204*I*e^(6*I*d*x + 6*I*c) - 80*I*e^(4*I*d*x + 4*I*c) + 300*I*e^(2*I*d*x + 2*I*c) - 30*I) + 15*(a*d*e^(7*I*d*x + 7*I*c) - 3*a*d*e^(5*I*d*x + 5*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(2*I/(a*d^2))*log(1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 15*(a*d*e^(7*I*d*x + 7*I*c) - 3*a*d*e^(5*I*d*x + 5*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(2*I/(a*d^2))*log(-1/4*I*a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a*d*e^(7*I*d*x + 7*I*c) - 3*a*d*e^(5*I*d*x + 5*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))","B",0
218,1,612,0,0.694472," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + 3 \, a^{2} d \sqrt{-\frac{9 i}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{104 \, {\left(6 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{-\frac{9 i}{a^{3} d^{2}}}\right)}}{1815 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) - 3 \, a^{2} d \sqrt{-\frac{9 i}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{104 \, {\left(6 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} - {\left(3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{-\frac{9 i}{a^{3} d^{2}}}\right)}}{1815 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(28 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + 3*a^2*d*sqrt(-9*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(104/1815*(6*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (3*a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(-9*I/(a^3*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(-9*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(104/1815*(6*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) - (3*a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(-9*I/(a^3*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(28*e^(4*I*d*x + 4*I*c) + 15*e^(2*I*d*x + 2*I*c) - 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
219,1,611,0,0.661645," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{2} i \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{1}{2} i \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, a^{2} d \sqrt{\frac{4 i}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{208 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(156 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 52 i \, a^{2} d\right)} \sqrt{\frac{4 i}{a^{3} d^{2}}}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + 3 \, a^{2} d \sqrt{\frac{4 i}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{208 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(-156 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 52 i \, a^{2} d\right)} \sqrt{\frac{4 i}{a^{3} d^{2}}}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(10 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 9 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/2*I*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-1/2*I*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(4*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/605*(208*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (156*I*a^2*d*e^(2*I*d*x + 2*I*c) - 52*I*a^2*d)*sqrt(4*I/(a^3*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + 3*a^2*d*sqrt(4*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/605*(208*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (-156*I*a^2*d*e^(2*I*d*x + 2*I*c) + 52*I*a^2*d)*sqrt(4*I/(a^3*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(10*I*e^(4*I*d*x + 4*I*c) + 9*I*e^(2*I*d*x + 2*I*c) - I))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
220,1,321,0,1.071629," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(4 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(4*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) - 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
221,1,320,0,0.581577," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{2} i \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{1}{2} i \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(2 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/2*I*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-1/2*I*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(2*I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c) + I))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
222,1,320,0,0.566372," ","integrate(1/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(8 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(8*e^(4*I*d*x + 4*I*c) + 9*e^(2*I*d*x + 2*I*c) + 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
223,1,382,0,0.692504," ","integrate(1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-38 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 25 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 14 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} - 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} \log\left(\frac{1}{2} i \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} \log\left(-\frac{1}{2} i \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{12 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/12*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-38*I*e^(6*I*d*x + 6*I*c) - 25*I*e^(4*I*d*x + 4*I*c) + 14*I*e^(2*I*d*x + 2*I*c) + I) - 3*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/2*I/(a^3*d^2))*log(1/2*I*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + 3*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(1/2*I/(a^3*d^2))*log(-1/2*I*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))","B",0
224,1,435,0,0.611151," ","integrate(1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(52 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 35 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 69 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 19 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + 3 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} \log\left(\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 3 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} \log\left(-\frac{1}{2} \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{12 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 2 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"-1/12*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(52*e^(8*I*d*x + 8*I*c) - 35*e^(6*I*d*x + 6*I*c) - 69*e^(4*I*d*x + 4*I*c) + 19*e^(2*I*d*x + 2*I*c) + 1) + 3*(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-1/2*I/(a^3*d^2))*log(1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 3*(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-1/2*I/(a^3*d^2))*log(-1/2*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a^2*d*e^(7*I*d*x + 7*I*c) - 2*a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))","B",0
225,1,621,0,0.846911," ","integrate(tan(d*x+c)^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + 30 \, a^{3} d \sqrt{\frac{25 i}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{1040 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(312 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 104 i \, a^{3} d\right)} \sqrt{\frac{25 i}{a^{5} d^{2}}}}{3025 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) - 30 \, a^{3} d \sqrt{\frac{25 i}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{1040 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(-312 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 104 i \, a^{3} d\right)} \sqrt{\frac{25 i}{a^{5} d^{2}}}}{3025 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(403 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 252 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 28 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + 30*a^3*d*sqrt(25*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/3025*(1040*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (312*I*a^3*d*e^(2*I*d*x + 2*I*c) - 104*I*a^3*d)*sqrt(25*I/(a^5*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) - 30*a^3*d*sqrt(25*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(1/3025*(1040*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (-312*I*a^3*d*e^(2*I*d*x + 2*I*c) + 104*I*a^3*d)*sqrt(25*I/(a^5*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(403*I*e^(6*I*d*x + 6*I*c) + 252*I*e^(4*I*d*x + 4*I*c) - 28*I*e^(2*I*d*x + 2*I*c) + 3*I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
226,1,621,0,0.739746," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(10 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 10 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 10 \, a^{3} d \sqrt{-\frac{4 i}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} + {\left(3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{-\frac{4 i}{a^{5} d^{2}}}\right)}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + 10 \, a^{3} d \sqrt{-\frac{4 i}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{52 \, {\left(4 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} - {\left(3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{-\frac{4 i}{a^{5} d^{2}}}\right)}}{605 \, {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(41 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 34 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 6 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{3} d}"," ",0,"1/40*(10*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 10*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 10*a^3*d*sqrt(-4*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(52/605*(4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) + (3*a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(-4*I/(a^5*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + 10*a^3*d*sqrt(-4*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(52/605*(4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c)) - (3*a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(-4*I/(a^5*d^2)))/(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(41*e^(6*I*d*x + 6*I*c) + 34*e^(4*I*d*x + 4*I*c) - 6*e^(2*I*d*x + 2*I*c) + 1))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
227,1,332,0,0.753652," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-23 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 12 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-23*I*e^(6*I*d*x + 6*I*c) - 12*I*e^(4*I*d*x + 4*I*c) + 8*I*e^(2*I*d*x + 2*I*c) - 3*I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
228,1,331,0,0.770483," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(17 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 18 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(17*e^(6*I*d*x + 6*I*c) + 18*e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) - 3))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
229,1,331,0,0.578314," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(10 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 10 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{3} d}"," ",0,"1/40*(10*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 10*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(6*I*d*x + 6*I*c) + 4*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) + I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
230,1,330,0,0.585286," ","integrate(1/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(83 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 102 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 22 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(83*e^(6*I*d*x + 6*I*c) + 102*e^(4*I*d*x + 4*I*c) + 22*e^(2*I*d*x + 2*I*c) + 3))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
231,1,393,0,0.612350," ","integrate(1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-463 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 269 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 220 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 29 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} - 30 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} \log\left(i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) + 30 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} \log\left(-i \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{120 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"1/120*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-463*I*e^(8*I*d*x + 8*I*c) - 269*I*e^(6*I*d*x + 6*I*c) + 220*I*e^(4*I*d*x + 4*I*c) + 29*I*e^(2*I*d*x + 2*I*c) + 3*I) - 30*(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/8*I/(a^5*d^2))*log(I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) + 30*(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(1/8*I/(a^5*d^2))*log(-I*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))","B",0
232,1,445,0,0.605732," ","integrate(1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(983 \, e^{\left(10 i \, d x + 10 i \, c\right)} - 544 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 1179 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 381 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 36 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)} + 30 \, {\left(a^{3} d e^{\left(9 i \, d x + 9 i \, c\right)} - 2 \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} \log\left(a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right) - 30 \, {\left(a^{3} d e^{\left(9 i \, d x + 9 i \, c\right)} - 2 \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} \log\left(-a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(i \, d x + i \, c\right)} + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)}{120 \, {\left(a^{3} d e^{\left(9 i \, d x + 9 i \, c\right)} - 2 \, a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"-1/120*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(983*e^(10*I*d*x + 10*I*c) - 544*e^(8*I*d*x + 8*I*c) - 1179*e^(6*I*d*x + 6*I*c) + 381*e^(4*I*d*x + 4*I*c) + 36*e^(2*I*d*x + 2*I*c) + 3) + 30*(a^3*d*e^(9*I*d*x + 9*I*c) - 2*a^3*d*e^(7*I*d*x + 7*I*c) + a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(-1/8*I/(a^5*d^2))*log(a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)) - 30*(a^3*d*e^(9*I*d*x + 9*I*c) - 2*a^3*d*e^(7*I*d*x + 7*I*c) + a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(-1/8*I/(a^5*d^2))*log(-a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(I*d*x + I*c) + 1/4*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)))/(a^3*d*e^(9*I*d*x + 9*I*c) - 2*a^3*d*e^(7*I*d*x + 7*I*c) + a^3*d*e^(5*I*d*x + 5*I*c))","B",0
233,1,643,0,0.644557," ","integrate(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{3} {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} + 3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - {\left(3 \, \sqrt{3} {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} - 3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - {\left(51 \, \sqrt{\frac{1}{3}} {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} - 17 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 17 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(51 \, \sqrt{\frac{1}{3}} {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} + 17 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 17 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(-34 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 34 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + {\left(-6 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + 6 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 17 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{24 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/24*((3*sqrt(3)*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) + 3*I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - (3*sqrt(3)*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) - 3*I*e^(4*I*d*x + 4*I*c) - 3*I*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - (51*sqrt(1/3)*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) - 17*I*e^(4*I*d*x + 4*I*c) - 17*I*e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (51*sqrt(1/3)*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) + 17*I*e^(4*I*d*x + 4*I*c) + 17*I*e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (-34*I*e^(4*I*d*x + 4*I*c) - 34*I*e^(2*I*d*x + 2*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + (-6*I*e^(4*I*d*x + 4*I*c) - 6*I*e^(2*I*d*x + 2*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + 6*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(10*e^(4*I*d*x + 4*I*c) + 17*e^(2*I*d*x + 2*I*c) + 1))/(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","B",0
234,1,492,0,0.624135," ","integrate(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(\sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 3 \, {\left(\sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - {\left(39 \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + 13 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(39 \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - 13 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 26 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-42 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{24 \, a d}"," ",0,"1/24*(3*(sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - I*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 3*(sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + I*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - (39*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + 13*I*e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (39*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - 13*I*e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 26*I*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 6*I*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-42*I*e^(2*I*d*x + 2*I*c) - 6*I))*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
235,1,491,0,0.728573," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(\sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 3 \, {\left(\sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - {\left(15 \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(15 \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 10 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) - 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + 6 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{24 \, a d}"," ",0,"-1/24*(3*(sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + I*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 3*(sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - I*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - (15*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - 5*I*e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (15*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + 5*I*e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 10*I*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) - 6*I*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + 6*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(e^(2*I*d*x + 2*I*c) + 1))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
236,1,493,0,0.608858," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(\sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 3 \, {\left(\sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - {\left(3 \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(3 \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{24 \, a d}"," ",0,"-1/24*(3*(sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - I*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 3*(sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + I*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - (3*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + I*e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (3*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - I*e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 2*I*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 6*I*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(6*I*e^(2*I*d*x + 2*I*c) + 6*I))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
237,1,488,0,0.619995," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(-3 i \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(3 i \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 5 \, {\left(-3 i \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 5 \, {\left(3 i \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 10 \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 6 \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + 6 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{24 \, a d}"," ",0,"1/24*((-3*I*sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - 3*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (3*I*sqrt(3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) - 3*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 5*(-3*I*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 5*(3*I*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2))*e^(2*I*d*x + 2*I*c) + e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 10*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 6*e^(2*I*d*x + 2*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + 6*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(e^(2*I*d*x + 2*I*c) + 1))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
238,1,644,0,0.637172," ","integrate(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(\sqrt{3} {\left(12 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} - 12 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} - 12 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 12 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(\sqrt{3} {\left(-12 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 12 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} - 12 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 12 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(-156 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 156 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} - 52 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 52 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(156 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} - 156 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} - 52 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 52 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 104 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} - e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 24 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} - e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + 4 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(-42 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 36 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)}}{96 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} - a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/96*((sqrt(3)*(12*I*a*d*e^(4*I*d*x + 4*I*c) - 12*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) - 12*e^(4*I*d*x + 4*I*c) + 12*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (sqrt(3)*(-12*I*a*d*e^(4*I*d*x + 4*I*c) + 12*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) - 12*e^(4*I*d*x + 4*I*c) + 12*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (sqrt(1/3)*(-156*I*a*d*e^(4*I*d*x + 4*I*c) + 156*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) - 52*e^(4*I*d*x + 4*I*c) + 52*e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (sqrt(1/3)*(156*I*a*d*e^(4*I*d*x + 4*I*c) - 156*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) - 52*e^(4*I*d*x + 4*I*c) + 52*e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 104*(e^(4*I*d*x + 4*I*c) - e^(2*I*d*x + 2*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 24*(e^(4*I*d*x + 4*I*c) - e^(2*I*d*x + 2*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + 4*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(-42*I*e^(4*I*d*x + 4*I*c) - 36*I*e^(2*I*d*x + 2*I*c) + 6*I))/(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))","B",0
239,1,781,0,0.667140," ","integrate(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(\sqrt{3} {\left(12 i \, a d e^{\left(6 i \, d x + 6 i \, c\right)} - 24 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 12 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} + 12 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 24 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 12 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(\sqrt{3} {\left(-12 i \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 24 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} - 12 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} + 12 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 24 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 12 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(-204 i \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 408 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} - 204 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} + 68 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 136 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 68 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(204 i \, a d e^{\left(6 i \, d x + 6 i \, c\right)} - 408 i \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 204 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{1}{a^{2} d^{2}}} + 68 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 136 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 68 \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a d \sqrt{\frac{1}{a^{2} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 136 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, e^{\left(4 i \, d x + 4 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) - 24 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, e^{\left(4 i \, d x + 4 i \, c\right)} + e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - 24 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(10 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 7 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 16 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{96 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/96*((sqrt(3)*(12*I*a*d*e^(6*I*d*x + 6*I*c) - 24*I*a*d*e^(4*I*d*x + 4*I*c) + 12*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) + 12*e^(6*I*d*x + 6*I*c) - 24*e^(4*I*d*x + 4*I*c) + 12*e^(2*I*d*x + 2*I*c))*log(1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (sqrt(3)*(-12*I*a*d*e^(6*I*d*x + 6*I*c) + 24*I*a*d*e^(4*I*d*x + 4*I*c) - 12*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) + 12*e^(6*I*d*x + 6*I*c) - 24*e^(4*I*d*x + 4*I*c) + 12*e^(2*I*d*x + 2*I*c))*log(-1/2*sqrt(3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (sqrt(1/3)*(-204*I*a*d*e^(6*I*d*x + 6*I*c) + 408*I*a*d*e^(4*I*d*x + 4*I*c) - 204*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) + 68*e^(6*I*d*x + 6*I*c) - 136*e^(4*I*d*x + 4*I*c) + 68*e^(2*I*d*x + 2*I*c))*log(3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (sqrt(1/3)*(204*I*a*d*e^(6*I*d*x + 6*I*c) - 408*I*a*d*e^(4*I*d*x + 4*I*c) + 204*I*a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/(a^2*d^2)) + 68*e^(6*I*d*x + 6*I*c) - 136*e^(4*I*d*x + 4*I*c) + 68*e^(2*I*d*x + 2*I*c))*log(-3/2*sqrt(1/3)*a*d*sqrt(1/(a^2*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 136*(e^(6*I*d*x + 6*I*c) - 2*e^(4*I*d*x + 4*I*c) + e^(2*I*d*x + 2*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) - 24*(e^(6*I*d*x + 6*I*c) - 2*e^(4*I*d*x + 4*I*c) + e^(2*I*d*x + 2*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - 24*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(10*e^(6*I*d*x + 6*I*c) - 7*e^(4*I*d*x + 4*I*c) - 16*e^(2*I*d*x + 2*I*c) + 1))/(a*d*e^(6*I*d*x + 6*I*c) - 2*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","B",0
240,1,684,0,0.620432," ","integrate(tan(d*x+c)^(14/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(45 \, \sqrt{3} {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} - 45 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 45 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - {\left(45 \, \sqrt{3} {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} + 45 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 45 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(3495 \, \sqrt{\frac{1}{3}} {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} + 1165 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 1165 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - {\left(3495 \, \sqrt{\frac{1}{3}} {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} - 1165 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 1165 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - {\left(2330 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2330 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) - {\left(-90 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 90 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-2373 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 3837 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 555 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 45 i\right)}}{720 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"-1/720*((45*sqrt(3)*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) - 45*I*e^(6*I*d*x + 6*I*c) - 45*I*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - (45*sqrt(3)*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) + 45*I*e^(6*I*d*x + 6*I*c) + 45*I*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (3495*sqrt(1/3)*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) + 1165*I*e^(6*I*d*x + 6*I*c) + 1165*I*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - (3495*sqrt(1/3)*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) - 1165*I*e^(6*I*d*x + 6*I*c) - 1165*I*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - (2330*I*e^(6*I*d*x + 6*I*c) + 2330*I*e^(4*I*d*x + 4*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) - (-90*I*e^(6*I*d*x + 6*I*c) - 90*I*e^(4*I*d*x + 4*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-2373*I*e^(6*I*d*x + 6*I*c) - 3837*I*e^(4*I*d*x + 4*I*c) - 555*I*e^(2*I*d*x + 2*I*c) + 45*I))/(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","B",0
241,1,521,0,0.507712," ","integrate(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + 89 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 89 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 178 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) - 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - 3 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(173 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 26 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{144 \, a^{2} d}"," ",0,"1/144*(9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + 89*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 89*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 178*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) - 18*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - 3*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(173*e^(4*I*d*x + 4*I*c) + 26*e^(2*I*d*x + 2*I*c) - 3))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
242,1,520,0,0.714297," ","integrate(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + 41 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 41 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 82 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(57 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 48 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 9 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{144 \, a^{2} d}"," ",0,"1/144*(9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + 41*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 41*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 82*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 18*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(57*I*e^(4*I*d*x + 4*I*c) + 48*I*e^(2*I*d*x + 2*I*c) - 9*I))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
243,1,521,0,0.548897," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 7 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 7 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 14 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) - 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - 3 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(5 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{144 \, a^{2} d}"," ",0,"-1/144*(9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 7*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 7*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 14*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) - 18*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - 3*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(5*e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) - 3))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
244,1,521,0,0.559654," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 9 \, {\left(\sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - 7 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 7 \, {\left(3 \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 14 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 9 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{144 \, a^{2} d}"," ",0,"-1/144*(9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 9*(sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) - 7*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) + I*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 7*(3*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - I*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 14*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 18*I*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(15*I*e^(4*I*d*x + 4*I*c) + 24*I*e^(2*I*d*x + 2*I*c) + 9*I))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
245,1,519,0,0.769517," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(-9 i \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - 9 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(9 i \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - 9 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(69 i \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - 23 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(-69 i \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} - 23 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 46 \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 18 \, e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + 3 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(17 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 20 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{144 \, a^{2} d}"," ",0,"1/144*((-9*I*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - 9*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (9*I*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - 9*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (69*I*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - 23*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (-69*I*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2))*e^(4*I*d*x + 4*I*c) - 23*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 46*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 18*e^(4*I*d*x + 4*I*c)*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + 3*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(17*e^(4*I*d*x + 4*I*c) + 20*e^(2*I*d*x + 2*I*c) + 3))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
246,1,685,0,0.600542," ","integrate(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{3} {\left(72 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - 72 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} - 72 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 72 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + 3 \, {\left(\sqrt{3} {\left(-72 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 72 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} - 72 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 72 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(-8568 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 8568 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} - 2856 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2856 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(8568 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - 8568 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} - 2856 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2856 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + 5712 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} - e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) + 432 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} - e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) + 24 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(-309 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 225 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 93 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 9 i\right)}}{3456 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/3456*(3*(sqrt(3)*(72*I*a^2*d*e^(6*I*d*x + 6*I*c) - 72*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) - 72*e^(6*I*d*x + 6*I*c) + 72*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + 3*(sqrt(3)*(-72*I*a^2*d*e^(6*I*d*x + 6*I*c) + 72*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) - 72*e^(6*I*d*x + 6*I*c) + 72*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (sqrt(1/3)*(-8568*I*a^2*d*e^(6*I*d*x + 6*I*c) + 8568*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) - 2856*e^(6*I*d*x + 6*I*c) + 2856*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (sqrt(1/3)*(8568*I*a^2*d*e^(6*I*d*x + 6*I*c) - 8568*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) - 2856*e^(6*I*d*x + 6*I*c) + 2856*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + 5712*(e^(6*I*d*x + 6*I*c) - e^(4*I*d*x + 4*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) + 432*(e^(6*I*d*x + 6*I*c) - e^(4*I*d*x + 4*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) + 24*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(-309*I*e^(6*I*d*x + 6*I*c) - 225*I*e^(4*I*d*x + 4*I*c) + 93*I*e^(2*I*d*x + 2*I*c) + 9*I))/(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))","B",0
247,1,832,0,0.949093," ","integrate(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{3} {\left(72 i \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} - 144 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 72 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} + 72 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 144 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 72 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + 3 \, {\left(\sqrt{3} {\left(-72 i \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 144 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - 72 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} + 72 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 144 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 72 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{1}{2} \, \sqrt{3} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(-13752 i \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 27504 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - 13752 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} + 4584 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 9168 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 4584 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + {\left(\sqrt{\frac{1}{3}} {\left(13752 i \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} - 27504 i \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 13752 i \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{1}{a^{4} d^{2}}} + 4584 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 9168 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 4584 \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(-\frac{3}{2} \, \sqrt{\frac{1}{3}} a^{2} d \sqrt{\frac{1}{a^{4} d^{2}}} + \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - 9168 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} - 2 \, e^{\left(6 i \, d x + 6 i \, c\right)} + e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} + i\right) - 432 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} - 2 \, e^{\left(6 i \, d x + 6 i \, c\right)} + e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(\left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} - i\right) - 72 \, \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(293 \, e^{\left(8 i \, d x + 8 i \, c\right)} - 110 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 368 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 38 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3\right)}}{3456 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} - 2 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/3456*(3*(sqrt(3)*(72*I*a^2*d*e^(8*I*d*x + 8*I*c) - 144*I*a^2*d*e^(6*I*d*x + 6*I*c) + 72*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) + 72*e^(8*I*d*x + 8*I*c) - 144*e^(6*I*d*x + 6*I*c) + 72*e^(4*I*d*x + 4*I*c))*log(1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + 3*(sqrt(3)*(-72*I*a^2*d*e^(8*I*d*x + 8*I*c) + 144*I*a^2*d*e^(6*I*d*x + 6*I*c) - 72*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) + 72*e^(8*I*d*x + 8*I*c) - 144*e^(6*I*d*x + 6*I*c) + 72*e^(4*I*d*x + 4*I*c))*log(-1/2*sqrt(3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + 1/2*I) + (sqrt(1/3)*(-13752*I*a^2*d*e^(8*I*d*x + 8*I*c) + 27504*I*a^2*d*e^(6*I*d*x + 6*I*c) - 13752*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) + 4584*e^(8*I*d*x + 8*I*c) - 9168*e^(6*I*d*x + 6*I*c) + 4584*e^(4*I*d*x + 4*I*c))*log(3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) + (sqrt(1/3)*(13752*I*a^2*d*e^(8*I*d*x + 8*I*c) - 27504*I*a^2*d*e^(6*I*d*x + 6*I*c) + 13752*I*a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(1/(a^4*d^2)) + 4584*e^(8*I*d*x + 8*I*c) - 9168*e^(6*I*d*x + 6*I*c) + 4584*e^(4*I*d*x + 4*I*c))*log(-3/2*sqrt(1/3)*a^2*d*sqrt(1/(a^4*d^2)) + ((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - 1/2*I) - 9168*(e^(8*I*d*x + 8*I*c) - 2*e^(6*I*d*x + 6*I*c) + e^(4*I*d*x + 4*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) + I) - 432*(e^(8*I*d*x + 8*I*c) - 2*e^(6*I*d*x + 6*I*c) + e^(4*I*d*x + 4*I*c))*log(((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(1/3) - I) - 72*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(293*e^(8*I*d*x + 8*I*c) - 110*e^(6*I*d*x + 6*I*c) - 368*e^(4*I*d*x + 4*I*c) + 38*e^(2*I*d*x + 2*I*c) + 3))/(a^2*d*e^(8*I*d*x + 8*I*c) - 2*a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","B",0
248,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,0,0,0,1.085117," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(2 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, a d e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-3 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 66 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 32 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 64 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 29 i \, e^{\left(i \, d x + i \, c\right)} - 2 i\right)}}{6 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 6 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, a d e^{\left(i \, d x + i \, c\right)} + 8 \, a d\right)}}, x\right)}{a d e^{\left(3 i \, d x + 3 i \, c\right)} - 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, a d e^{\left(i \, d x + i \, c\right)}}"," ",0,"(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(2*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) + 2*I) + (a*d*e^(3*I*d*x + 3*I*c) - 4*a*d*e^(2*I*d*x + 2*I*c) + 4*a*d*e^(I*d*x + I*c))*integral(1/6*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-3*I*e^(5*I*d*x + 5*I*c) + 66*I*e^(4*I*d*x + 4*I*c) - 32*I*e^(3*I*d*x + 3*I*c) + 64*I*e^(2*I*d*x + 2*I*c) - 29*I*e^(I*d*x + I*c) - 2*I)/(a*d*e^(5*I*d*x + 5*I*c) - 6*a*d*e^(4*I*d*x + 4*I*c) + 11*a*d*e^(3*I*d*x + 3*I*c) - 2*a*d*e^(2*I*d*x + 2*I*c) - 12*a*d*e^(I*d*x + I*c) + 8*a*d), x))/(a*d*e^(3*I*d*x + 3*I*c) - 4*a*d*e^(2*I*d*x + 2*I*c) + 4*a*d*e^(I*d*x + I*c))","F",0
262,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,0,0,0,0.687720," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, a d e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(3 \, e^{\left(5 i \, d x + 5 i \, c\right)} + 30 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 46 \, e^{\left(3 i \, d x + 3 i \, c\right)} - 20 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 43 \, e^{\left(i \, d x + i \, c\right)} - 50\right)}}{6 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 6 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, a d e^{\left(i \, d x + i \, c\right)} + 8 \, a d\right)}}, x\right)}{a d e^{\left(3 i \, d x + 3 i \, c\right)} - 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, a d e^{\left(i \, d x + i \, c\right)}}"," ",0,"(2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1) + (a*d*e^(3*I*d*x + 3*I*c) - 4*a*d*e^(2*I*d*x + 2*I*c) + 4*a*d*e^(I*d*x + I*c))*integral(1/6*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(3*e^(5*I*d*x + 5*I*c) + 30*e^(4*I*d*x + 4*I*c) + 46*e^(3*I*d*x + 3*I*c) - 20*e^(2*I*d*x + 2*I*c) + 43*e^(I*d*x + I*c) - 50)/(a*d*e^(5*I*d*x + 5*I*c) - 6*a*d*e^(4*I*d*x + 4*I*c) + 11*a*d*e^(3*I*d*x + 3*I*c) - 2*a*d*e^(2*I*d*x + 2*I*c) - 12*a*d*e^(I*d*x + I*c) + 8*a*d), x))/(a*d*e^(3*I*d*x + 3*I*c) - 4*a*d*e^(2*I*d*x + 2*I*c) + 4*a*d*e^(I*d*x + I*c))","F",0
264,-1,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,0,0,0,0.811606," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-19 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 12 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 34 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 11 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 12 i \, e^{\left(i \, d x + i \, c\right)} + 4 i\right)} + 2 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, a d e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(3 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 210 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 11 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 130 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, e^{\left(i \, d x + i \, c\right)} + 80 i\right)}}{6 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 6 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, a d e^{\left(i \, d x + i \, c\right)} + 8 \, a d\right)}}, x\right)}{2 \, {\left(a d e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 \, a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/2*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-19*I*e^(6*I*d*x + 6*I*c) + 12*I*e^(5*I*d*x + 5*I*c) - 34*I*e^(4*I*d*x + 4*I*c) + 24*I*e^(3*I*d*x + 3*I*c) - 11*I*e^(2*I*d*x + 2*I*c) + 12*I*e^(I*d*x + I*c) + 4*I) + 2*(a*d*e^(5*I*d*x + 5*I*c) - 4*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c) - 4*a*d*e^(I*d*x + I*c))*integral(1/6*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(3*I*e^(5*I*d*x + 5*I*c) - 210*I*e^(4*I*d*x + 4*I*c) + 11*I*e^(3*I*d*x + 3*I*c) - 130*I*e^(2*I*d*x + 2*I*c) + 8*I*e^(I*d*x + I*c) + 80*I)/(a*d*e^(5*I*d*x + 5*I*c) - 6*a*d*e^(4*I*d*x + 4*I*c) + 11*a*d*e^(3*I*d*x + 3*I*c) - 2*a*d*e^(2*I*d*x + 2*I*c) - 12*a*d*e^(I*d*x + I*c) + 8*a*d), x))/(a*d*e^(5*I*d*x + 5*I*c) - 4*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(3*I*d*x + 3*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c) - 4*a*d*e^(I*d*x + I*c))","F",0
266,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,0,0,0,3.785630," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(7 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 12 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 26 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 24 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 31 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 12 i \, e^{\left(i \, d x + i \, c\right)} + 12 i\right)} + 36 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-27 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 210 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 344 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 400 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 317 i \, e^{\left(i \, d x + i \, c\right)} + 190 i\right)}}{108 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, a^{2} d e^{\left(i \, d x + i \, c\right)} + 8 \, a^{2} d\right)}}, x\right)}{36 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/36*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(7*I*e^(6*I*d*x + 6*I*c) - 12*I*e^(5*I*d*x + 5*I*c) + 26*I*e^(4*I*d*x + 4*I*c) - 24*I*e^(3*I*d*x + 3*I*c) + 31*I*e^(2*I*d*x + 2*I*c) - 12*I*e^(I*d*x + I*c) + 12*I) + 36*(a^2*d*e^(5*I*d*x + 5*I*c) - 4*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(3*I*d*x + 3*I*c))*integral(1/108*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-27*I*e^(5*I*d*x + 5*I*c) + 210*I*e^(4*I*d*x + 4*I*c) - 344*I*e^(3*I*d*x + 3*I*c) + 400*I*e^(2*I*d*x + 2*I*c) - 317*I*e^(I*d*x + I*c) + 190*I)/(a^2*d*e^(5*I*d*x + 5*I*c) - 6*a^2*d*e^(4*I*d*x + 4*I*c) + 11*a^2*d*e^(3*I*d*x + 3*I*c) - 2*a^2*d*e^(2*I*d*x + 2*I*c) - 12*a^2*d*e^(I*d*x + I*c) + 8*a^2*d), x))/(a^2*d*e^(5*I*d*x + 5*I*c) - 4*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(3*I*d*x + 3*I*c))","F",0
268,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,0,0,0,0.917119," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(79 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 12 \, e^{\left(5 i \, d x + 5 i \, c\right)} + 170 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 24 \, e^{\left(3 i \, d x + 3 i \, c\right)} + 103 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, e^{\left(i \, d x + i \, c\right)} + 12\right)} + 36 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(27 \, e^{\left(5 i \, d x + 5 i \, c\right)} + 750 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 484 \, e^{\left(3 i \, d x + 3 i \, c\right)} + 40 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 457 \, e^{\left(i \, d x + i \, c\right)} - 710\right)}}{108 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, a^{2} d e^{\left(i \, d x + i \, c\right)} + 8 \, a^{2} d\right)}}, x\right)}{36 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/36*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(79*e^(6*I*d*x + 6*I*c) - 12*e^(5*I*d*x + 5*I*c) + 170*e^(4*I*d*x + 4*I*c) - 24*e^(3*I*d*x + 3*I*c) + 103*e^(2*I*d*x + 2*I*c) - 12*e^(I*d*x + I*c) + 12) + 36*(a^2*d*e^(5*I*d*x + 5*I*c) - 4*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(3*I*d*x + 3*I*c))*integral(1/108*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(27*e^(5*I*d*x + 5*I*c) + 750*e^(4*I*d*x + 4*I*c) + 484*e^(3*I*d*x + 3*I*c) + 40*e^(2*I*d*x + 2*I*c) + 457*e^(I*d*x + I*c) - 710)/(a^2*d*e^(5*I*d*x + 5*I*c) - 6*a^2*d*e^(4*I*d*x + 4*I*c) + 11*a^2*d*e^(3*I*d*x + 3*I*c) - 2*a^2*d*e^(2*I*d*x + 2*I*c) - 12*a^2*d*e^(I*d*x + I*c) + 8*a^2*d), x))/(a^2*d*e^(5*I*d*x + 5*I*c) - 4*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(3*I*d*x + 3*I*c))","F",0
270,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,0,0,0,0.561674," ","integrate(1/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-421 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 228 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 703 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 444 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 131 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 204 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 163 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 12 i \, e^{\left(i \, d x + i \, c\right)} + 12 i\right)} + 36 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(27 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 4530 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 286 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 2380 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 313 i \, e^{\left(i \, d x + i \, c\right)} + 2150 i\right)}}{108 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 12 \, a^{2} d e^{\left(i \, d x + i \, c\right)} + 8 \, a^{2} d\right)}}, x\right)}{36 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/36*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-421*I*e^(8*I*d*x + 8*I*c) + 228*I*e^(7*I*d*x + 7*I*c) - 703*I*e^(6*I*d*x + 6*I*c) + 444*I*e^(5*I*d*x + 5*I*c) - 131*I*e^(4*I*d*x + 4*I*c) + 204*I*e^(3*I*d*x + 3*I*c) + 163*I*e^(2*I*d*x + 2*I*c) - 12*I*e^(I*d*x + I*c) + 12*I) + 36*(a^2*d*e^(7*I*d*x + 7*I*c) - 4*a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(5*I*d*x + 5*I*c) + 4*a^2*d*e^(4*I*d*x + 4*I*c) - 4*a^2*d*e^(3*I*d*x + 3*I*c))*integral(1/108*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(27*I*e^(5*I*d*x + 5*I*c) - 4530*I*e^(4*I*d*x + 4*I*c) - 286*I*e^(3*I*d*x + 3*I*c) - 2380*I*e^(2*I*d*x + 2*I*c) - 313*I*e^(I*d*x + I*c) + 2150*I)/(a^2*d*e^(5*I*d*x + 5*I*c) - 6*a^2*d*e^(4*I*d*x + 4*I*c) + 11*a^2*d*e^(3*I*d*x + 3*I*c) - 2*a^2*d*e^(2*I*d*x + 2*I*c) - 12*a^2*d*e^(I*d*x + I*c) + 8*a^2*d), x))/(a^2*d*e^(7*I*d*x + 7*I*c) - 4*a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(5*I*d*x + 5*I*c) + 4*a^2*d*e^(4*I*d*x + 4*I*c) - 4*a^2*d*e^(3*I*d*x + 3*I*c))","F",0
272,1,403,0,0.660181," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","-\frac{3 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(15 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 21 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 14\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left({\left(7 i \, \sqrt{3} d - 7 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(14 i \, \sqrt{3} d - 14 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, \sqrt{3} d - 7 \, d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left({\left(-7 i \, \sqrt{3} d - 7 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-14 i \, \sqrt{3} d - 14 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 7 i \, \sqrt{3} d - 7 \, d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 14 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)}{14 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/14*(3*2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(15*e^(4*I*d*x + 4*I*c) + 21*e^(2*I*d*x + 2*I*c) + 14)*e^(2/3*I*d*x + 2/3*I*c) - (1/4)^(1/3)*((7*I*sqrt(3)*d - 7*d)*e^(4*I*d*x + 4*I*c) + (14*I*sqrt(3)*d - 14*d)*e^(2*I*d*x + 2*I*c) + 7*I*sqrt(3)*d - 7*d)*(-a/d^3)^(1/3)*log((1/4)^(1/3)*(I*sqrt(3)*d - d)*(-a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - (1/4)^(1/3)*((-7*I*sqrt(3)*d - 7*d)*e^(4*I*d*x + 4*I*c) + (-14*I*sqrt(3)*d - 14*d)*e^(2*I*d*x + 2*I*c) - 7*I*sqrt(3)*d - 7*d)*(-a/d^3)^(1/3)*log((1/4)^(1/3)*(-I*sqrt(3)*d - d)*(-a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 14*(1/4)^(1/3)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*(-a/d^3)^(1/3)*log(2*(1/4)^(1/3)*d*(-a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
273,1,294,0,0.566285," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{{\left({\left(i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, \sqrt{3} d - d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(\sqrt{3} d + i \, d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + {\left({\left(-i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, \sqrt{3} d - d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(\sqrt{3} d - i \, d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - 2 i \, d \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) - 3 i \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{8}{3} i \, d x + \frac{8}{3} i \, c\right)}}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2*(((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d - d)*(1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (sqrt(3)*d + I*d)*(1/4*I*a/d^3)^(1/3)) + ((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d - d)*(1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (sqrt(3)*d - I*d)*(1/4*I*a/d^3)^(1/3)) + 2*(d*e^(2*I*d*x + 2*I*c) + d)*(1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 2*I*d*(1/4*I*a/d^3)^(1/3)) - 3*I*2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(8/3*I*d*x + 8/3*I*c))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
274,1,239,0,1.572755," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(-2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 6 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}}{2 \, d}"," ",0,"1/2*((1/4)^(1/3)*(-I*sqrt(3)*d - d)*(a/d^3)^(1/3)*log((1/4)^(1/3)*(I*sqrt(3)*d + d)*(a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + (1/4)^(1/3)*(I*sqrt(3)*d - d)*(a/d^3)^(1/3)*log((1/4)^(1/3)*(-I*sqrt(3)*d + d)*(a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 2*(1/4)^(1/3)*d*(a/d^3)^(1/3)*log(-2*(1/4)^(1/3)*d*(a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 6*2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c))/d","A",0
275,1,188,0,1.476738," ","integrate((a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(-\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(\sqrt{3} d + i \, d\right)} \left(-\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(-\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(\sqrt{3} d - i \, d\right)} \left(-\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + \left(-\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2 i \, d \left(-\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right)"," ",0,"1/2*(I*sqrt(3) - 1)*(-1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (sqrt(3)*d + I*d)*(-1/4*I*a/d^3)^(1/3)) + 1/2*(-I*sqrt(3) - 1)*(-1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (sqrt(3)*d - I*d)*(-1/4*I*a/d^3)^(1/3)) + (-1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2*I*d*(-1/4*I*a/d^3)^(1/3))","A",0
276,1,387,0,0.700171," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \frac{1}{2} \, {\left(i \, \sqrt{3} d + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}}\right) + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \frac{1}{2} \, {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}}\right) + \left(\frac{1}{4}\right)^{\frac{1}{3}} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - d \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}}\right)"," ",0,"1/2*(1/4)^(1/3)*(I*sqrt(3) - 1)*(-a/d^3)^(1/3)*log((1/4)^(1/3)*(I*sqrt(3)*d - d)*(-a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 1/2*(1/4)^(1/3)*(-I*sqrt(3) - 1)*(-a/d^3)^(1/3)*log((1/4)^(1/3)*(-I*sqrt(3)*d - d)*(-a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 1/2*(-I*sqrt(3) - 1)*(a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 1/2*(I*sqrt(3)*d + d)*(a/d^3)^(1/3)) + 1/2*(I*sqrt(3) - 1)*(a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 1/2*(-I*sqrt(3)*d + d)*(a/d^3)^(1/3)) + (1/4)^(1/3)*(-a/d^3)^(1/3)*log(2*(1/4)^(1/3)*d*(-a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + (a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - d*(a/d^3)^(1/3))","B",0
277,1,550,0,1.672741," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(-2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left({\left(i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, \sqrt{3} d + d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(\sqrt{3} d + i \, d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + {\left({\left(-i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, \sqrt{3} d + d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(\sqrt{3} d - i \, d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - 2 i \, d \left(\frac{i \, a}{4 \, d^{3}}\right)^{\frac{1}{3}}\right) + {\left({\left(i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, \sqrt{3} d + d\right)} \left(-\frac{i \, a}{27 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - \frac{3}{2} \, {\left(\sqrt{3} d + i \, d\right)} \left(-\frac{i \, a}{27 \, d^{3}}\right)^{\frac{1}{3}}\right) + {\left({\left(-i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, \sqrt{3} d + d\right)} \left(-\frac{i \, a}{27 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \frac{3}{2} \, {\left(\sqrt{3} d - i \, d\right)} \left(-\frac{i \, a}{27 \, d^{3}}\right)^{\frac{1}{3}}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \left(-\frac{i \, a}{27 \, d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 3 i \, d \left(-\frac{i \, a}{27 \, d^{3}}\right)^{\frac{1}{3}}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/2*(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(-2*I*e^(2*I*d*x + 2*I*c) - 2*I)*e^(2/3*I*d*x + 2/3*I*c) + ((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d + d)*(1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (sqrt(3)*d + I*d)*(1/4*I*a/d^3)^(1/3)) + ((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d + d)*(1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (sqrt(3)*d - I*d)*(1/4*I*a/d^3)^(1/3)) + 2*(d*e^(2*I*d*x + 2*I*c) - d)*(1/4*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 2*I*d*(1/4*I*a/d^3)^(1/3)) + ((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d + d)*(-1/27*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 3/2*(sqrt(3)*d + I*d)*(-1/27*I*a/d^3)^(1/3)) + ((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d + d)*(-1/27*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 3/2*(sqrt(3)*d - I*d)*(-1/27*I*a/d^3)^(1/3)) + 2*(d*e^(2*I*d*x + 2*I*c) - d)*(-1/27*I*a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 3*I*d*(-1/27*I*a/d^3)^(1/3)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
278,1,694,0,0.497824," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{18 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(2 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 9 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left({\left(-3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, \sqrt{3} d - 3 \, d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 9 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left({\left(3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, \sqrt{3} d - 3 \, d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 54 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(-2 \, \left(\frac{1}{4}\right)^{\frac{1}{3}} d \left(\frac{a}{d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 8 \, {\left({\left(3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, \sqrt{3} d - 3 \, d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \frac{1}{18} \, {\left(9 i \, \sqrt{3} d - 9 \, d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}}\right) + 8 \, {\left({\left(-3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, \sqrt{3} d - 3 \, d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \frac{1}{18} \, {\left(-9 i \, \sqrt{3} d - 9 \, d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}}\right) + 48 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + d \left(-\frac{a}{d^{3}}\right)^{\frac{1}{3}}\right)}{54 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/54*(18*2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(2*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*e^(2/3*I*d*x + 2/3*I*c) + 9*(1/4)^(1/3)*((-3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) - 3*I*sqrt(3)*d - 3*d)*(a/d^3)^(1/3)*log((1/4)^(1/3)*(I*sqrt(3)*d + d)*(a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 9*(1/4)^(1/3)*((3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (-6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) + 3*I*sqrt(3)*d - 3*d)*(a/d^3)^(1/3)*log((1/4)^(1/3)*(-I*sqrt(3)*d + d)*(a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 54*(1/4)^(1/3)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*(a/d^3)^(1/3)*log(-2*(1/4)^(1/3)*d*(a/d^3)^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 8*((3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (-6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) + 3*I*sqrt(3)*d - 3*d)*(-a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 1/18*(9*I*sqrt(3)*d - 9*d)*(-a/d^3)^(1/3)) + 8*((-3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) - 3*I*sqrt(3)*d - 3*d)*(-a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 1/18*(-9*I*sqrt(3)*d - 9*d)*(-a/d^3)^(1/3)) + 48*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*(-a/d^3)^(1/3)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + d*(-a/d^3)^(1/3)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
279,1,226,0,0.477443," ","integrate((a+I*a*tan(d*x+c))^(2/3),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(-\frac{i \, a^{2}}{2 \, d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(i \, \sqrt{3} d^{2} - d^{2}\right)} \left(-\frac{i \, a^{2}}{2 \, d^{3}}\right)^{\frac{2}{3}}}{a}\right) + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(-\frac{i \, a^{2}}{2 \, d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(-i \, \sqrt{3} d^{2} - d^{2}\right)} \left(-\frac{i \, a^{2}}{2 \, d^{3}}\right)^{\frac{2}{3}}}{a}\right) + \left(-\frac{i \, a^{2}}{2 \, d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \, d^{2} \left(-\frac{i \, a^{2}}{2 \, d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}}{a}\right)"," ",0,"1/2*(-I*sqrt(3) - 1)*(-1/2*I*a^2/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (I*sqrt(3)*d^2 - d^2)*(-1/2*I*a^2/d^3)^(2/3))/a) + 1/2*(I*sqrt(3) - 1)*(-1/2*I*a^2/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (-I*sqrt(3)*d^2 - d^2)*(-1/2*I*a^2/d^3)^(2/3))/a) + (-1/2*I*a^2/d^3)^(1/3)*log((2*d^2*(-1/2*I*a^2/d^3)^(2/3) + 2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c))/a)","B",0
280,1,513,0,0.472876," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","-\frac{3 \cdot 2^{\frac{1}{3}} {\left(121 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 240 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 245 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 70 \, a\right)} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - 2^{\frac{1}{3}} {\left({\left(35 i \, \sqrt{3} d - 35 \, d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(105 i \, \sqrt{3} d - 105 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(105 i \, \sqrt{3} d - 105 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 35 i \, \sqrt{3} d - 35 \, d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) - 2^{\frac{1}{3}} {\left({\left(-35 i \, \sqrt{3} d - 35 \, d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-105 i \, \sqrt{3} d - 105 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-105 i \, \sqrt{3} d - 105 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 35 i \, \sqrt{3} d - 35 \, d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) - 70 \cdot 2^{\frac{1}{3}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)}{70 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/70*(3*2^(1/3)*(121*a*e^(6*I*d*x + 6*I*c) + 240*a*e^(4*I*d*x + 4*I*c) + 245*a*e^(2*I*d*x + 2*I*c) + 70*a)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 2^(1/3)*((35*I*sqrt(3)*d - 35*d)*e^(6*I*d*x + 6*I*c) + (105*I*sqrt(3)*d - 105*d)*e^(4*I*d*x + 4*I*c) + (105*I*sqrt(3)*d - 105*d)*e^(2*I*d*x + 2*I*c) + 35*I*sqrt(3)*d - 35*d)*(-a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(I*sqrt(3)*d - d)*(-a^4/d^3)^(1/3))/a) - 2^(1/3)*((-35*I*sqrt(3)*d - 35*d)*e^(6*I*d*x + 6*I*c) + (-105*I*sqrt(3)*d - 105*d)*e^(4*I*d*x + 4*I*c) + (-105*I*sqrt(3)*d - 105*d)*e^(2*I*d*x + 2*I*c) - 35*I*sqrt(3)*d - 35*d)*(-a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(-I*sqrt(3)*d - d)*(-a^4/d^3)^(1/3))/a) - 70*2^(1/3)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*(-a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(-a^4/d^3)^(1/3)*d)/a))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
281,1,416,0,0.477846," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{2^{\frac{1}{3}} {\left(-66 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 84 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 42 i \, a\right)} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left({\left(7 i \, \sqrt{3} d - 7 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(14 i \, \sqrt{3} d - 14 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, \sqrt{3} d - 7 \, d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(\sqrt{3} d + i \, d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + {\left({\left(-7 i \, \sqrt{3} d - 7 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-14 i \, \sqrt{3} d - 14 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 7 i \, \sqrt{3} d - 7 \, d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(\sqrt{3} d - i \, d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 14 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - i \, \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)}{14 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/14*(2^(1/3)*(-66*I*a*e^(4*I*d*x + 4*I*c) - 84*I*a*e^(2*I*d*x + 2*I*c) - 42*I*a)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + ((7*I*sqrt(3)*d - 7*d)*e^(4*I*d*x + 4*I*c) + (14*I*sqrt(3)*d - 14*d)*e^(2*I*d*x + 2*I*c) + 7*I*sqrt(3)*d - 7*d)*(2*I*a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (sqrt(3)*d + I*d)*(2*I*a^4/d^3)^(1/3))/a) + ((-7*I*sqrt(3)*d - 7*d)*e^(4*I*d*x + 4*I*c) + (-14*I*sqrt(3)*d - 14*d)*e^(2*I*d*x + 2*I*c) - 7*I*sqrt(3)*d - 7*d)*(2*I*a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (sqrt(3)*d - I*d)*(2*I*a^4/d^3)^(1/3))/a) + 14*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*(2*I*a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - I*(2*I*a^4/d^3)^(1/3)*d)/a))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
282,1,350,0,0.443872," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{3 \cdot 2^{\frac{1}{3}} {\left(3 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 2 \, a\right)} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left({\left(-i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, \sqrt{3} d - d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(i \, \sqrt{3} d + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 2^{\frac{1}{3}} {\left({\left(i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, \sqrt{3} d - d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 2 \cdot 2^{\frac{1}{3}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - 2^{\frac{1}{3}} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2*(3*2^(1/3)*(3*a*e^(2*I*d*x + 2*I*c) + 2*a)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d - d)*(a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(I*sqrt(3)*d + d)*(a^4/d^3)^(1/3))/a) + 2^(1/3)*((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d - d)*(a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(-I*sqrt(3)*d + d)*(a^4/d^3)^(1/3))/a) + 2*2^(1/3)*(d*e^(2*I*d*x + 2*I*c) + d)*(a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 2^(1/3)*(a^4/d^3)^(1/3)*d)/a))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
283,1,262,0,0.484878," ","integrate((a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{6 i \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(i \, \sqrt{3} d - d\right)} \left(-\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(\sqrt{3} d + i \, d\right)} \left(-\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + {\left(-i \, \sqrt{3} d - d\right)} \left(-\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(\sqrt{3} d - i \, d\right)} \left(-\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 2 \, \left(-\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} d \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + i \, \left(-\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)}{2 \, d}"," ",0,"1/2*(6*I*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (I*sqrt(3)*d - d)*(-2*I*a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (sqrt(3)*d + I*d)*(-2*I*a^4/d^3)^(1/3))/a) + (-I*sqrt(3)*d - d)*(-2*I*a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (sqrt(3)*d - I*d)*(-2*I*a^4/d^3)^(1/3))/a) + 2*(-2*I*a^4/d^3)^(1/3)*d*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + I*(-2*I*a^4/d^3)^(1/3)*d)/a))/d","B",0
284,1,446,0,0.467625," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{1}{2} \cdot 2^{\frac{1}{3}} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + \frac{1}{2} \cdot 2^{\frac{1}{3}} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + \frac{1}{2} \, \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(i \, \sqrt{3} d + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + \frac{1}{2} \, \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 2^{\frac{1}{3}} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right) + \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)"," ",0,"1/2*2^(1/3)*(-a^4/d^3)^(1/3)*(I*sqrt(3) - 1)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(I*sqrt(3)*d - d)*(-a^4/d^3)^(1/3))/a) + 1/2*2^(1/3)*(-a^4/d^3)^(1/3)*(-I*sqrt(3) - 1)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(-I*sqrt(3)*d - d)*(-a^4/d^3)^(1/3))/a) + 1/2*(a^4/d^3)^(1/3)*(-I*sqrt(3) - 1)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (I*sqrt(3)*d + d)*(a^4/d^3)^(1/3))/a) + 1/2*(a^4/d^3)^(1/3)*(I*sqrt(3) - 1)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (-I*sqrt(3)*d + d)*(a^4/d^3)^(1/3))/a) + 2^(1/3)*(-a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(-a^4/d^3)^(1/3)*d)/a) + (a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (a^4/d^3)^(1/3)*d)/a)","B",0
285,1,617,0,0.451437," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{2^{\frac{1}{3}} {\left(-2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a\right)} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left({\left(i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, \sqrt{3} d + d\right)} \left(-\frac{64 i \, a^{4}}{27 \, d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{8 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - 3 \, {\left(\sqrt{3} d + i \, d\right)} \left(-\frac{64 i \, a^{4}}{27 \, d^{3}}\right)^{\frac{1}{3}}}{8 \, a}\right) + {\left({\left(-i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, \sqrt{3} d + d\right)} \left(-\frac{64 i \, a^{4}}{27 \, d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{8 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 3 \, {\left(\sqrt{3} d - i \, d\right)} \left(-\frac{64 i \, a^{4}}{27 \, d^{3}}\right)^{\frac{1}{3}}}{8 \, a}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \left(-\frac{64 i \, a^{4}}{27 \, d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{4 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 3 i \, \left(-\frac{64 i \, a^{4}}{27 \, d^{3}}\right)^{\frac{1}{3}} d}{4 \, a}\right) + {\left({\left(i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, \sqrt{3} d + d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(\sqrt{3} d + i \, d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + {\left({\left(-i \, \sqrt{3} d - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, \sqrt{3} d + d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(\sqrt{3} d - i \, d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - i \, \left(\frac{2 i \, a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/2*(2^(1/3)*(-2*I*a*e^(2*I*d*x + 2*I*c) - 2*I*a)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + ((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d + d)*(-64/27*I*a^4/d^3)^(1/3)*log(1/8*(8*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 3*(sqrt(3)*d + I*d)*(-64/27*I*a^4/d^3)^(1/3))/a) + ((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d + d)*(-64/27*I*a^4/d^3)^(1/3)*log(1/8*(8*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 3*(sqrt(3)*d - I*d)*(-64/27*I*a^4/d^3)^(1/3))/a) + 2*(d*e^(2*I*d*x + 2*I*c) - d)*(-64/27*I*a^4/d^3)^(1/3)*log(1/4*(4*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 3*I*(-64/27*I*a^4/d^3)^(1/3)*d)/a) + ((I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) - I*sqrt(3)*d + d)*(2*I*a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (sqrt(3)*d + I*d)*(2*I*a^4/d^3)^(1/3))/a) + ((-I*sqrt(3)*d - d)*e^(2*I*d*x + 2*I*c) + I*sqrt(3)*d + d)*(2*I*a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (sqrt(3)*d - I*d)*(2*I*a^4/d^3)^(1/3))/a) + 2*(d*e^(2*I*d*x + 2*I*c) - d)*(2*I*a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - I*(2*I*a^4/d^3)^(1/3)*d)/a))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
286,1,758,0,0.465533," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{18 \cdot 2^{\frac{1}{3}} {\left(5 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, a\right)} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 9 \cdot 2^{\frac{1}{3}} {\left({\left(-3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, \sqrt{3} d - 3 \, d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(i \, \sqrt{3} d + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 9 \cdot 2^{\frac{1}{3}} {\left({\left(3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, \sqrt{3} d - 3 \, d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 2^{\frac{1}{3}} {\left(-i \, \sqrt{3} d + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{2 \, a}\right) + 54 \cdot 2^{\frac{1}{3}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - 2^{\frac{1}{3}} \left(\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right) + 11 \, {\left({\left(3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, \sqrt{3} d - 3 \, d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{18 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(9 i \, \sqrt{3} d - 9 \, d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{18 \, a}\right) + 11 \, {\left({\left(-3 i \, \sqrt{3} d - 3 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(6 i \, \sqrt{3} d + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, \sqrt{3} d - 3 \, d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{18 \cdot 2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(-9 i \, \sqrt{3} d - 9 \, d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}}}{18 \, a}\right) + 66 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \left(-\frac{a^{4}}{d^{3}}\right)^{\frac{1}{3}} d}{a}\right)}{54 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/54*(18*2^(1/3)*(5*a*e^(4*I*d*x + 4*I*c) + 3*a*e^(2*I*d*x + 2*I*c) - 2*a)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 9*2^(1/3)*((-3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) - 3*I*sqrt(3)*d - 3*d)*(a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(I*sqrt(3)*d + d)*(a^4/d^3)^(1/3))/a) + 9*2^(1/3)*((3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (-6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) + 3*I*sqrt(3)*d - 3*d)*(a^4/d^3)^(1/3)*log(1/2*(2*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + 2^(1/3)*(-I*sqrt(3)*d + d)*(a^4/d^3)^(1/3))/a) + 54*2^(1/3)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*(a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - 2^(1/3)*(a^4/d^3)^(1/3)*d)/a) + 11*((3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (-6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) + 3*I*sqrt(3)*d - 3*d)*(-a^4/d^3)^(1/3)*log(1/18*(18*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (9*I*sqrt(3)*d - 9*d)*(-a^4/d^3)^(1/3))/a) + 11*((-3*I*sqrt(3)*d - 3*d)*e^(4*I*d*x + 4*I*c) + (6*I*sqrt(3)*d + 6*d)*e^(2*I*d*x + 2*I*c) - 3*I*sqrt(3)*d - 3*d)*(-a^4/d^3)^(1/3)*log(1/18*(18*2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (-9*I*sqrt(3)*d - 9*d)*(-a^4/d^3)^(1/3))/a) + 66*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*(-a^4/d^3)^(1/3)*log((2^(1/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (-a^4/d^3)^(1/3)*d)/a))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
287,1,280,0,0.431375," ","integrate((a+I*a*tan(d*x+c))^(5/3),x, algorithm=""fricas"")","\frac{3 i \cdot 2^{\frac{2}{3}} a \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + \left(-\frac{4 i \, a^{5}}{d^{3}}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} d - d\right)} \log\left(\frac{4 \cdot 2^{\frac{1}{3}} a^{3} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(i \, \sqrt{3} d^{2} - d^{2}\right)} \left(-\frac{4 i \, a^{5}}{d^{3}}\right)^{\frac{2}{3}}}{4 \, a^{3}}\right) + \left(-\frac{4 i \, a^{5}}{d^{3}}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} d - d\right)} \log\left(\frac{4 \cdot 2^{\frac{1}{3}} a^{3} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(-i \, \sqrt{3} d^{2} - d^{2}\right)} \left(-\frac{4 i \, a^{5}}{d^{3}}\right)^{\frac{2}{3}}}{4 \, a^{3}}\right) + 2 \, \left(-\frac{4 i \, a^{5}}{d^{3}}\right)^{\frac{1}{3}} d \log\left(\frac{2 \cdot 2^{\frac{1}{3}} a^{3} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + \left(-\frac{4 i \, a^{5}}{d^{3}}\right)^{\frac{2}{3}} d^{2}}{2 \, a^{3}}\right)}{2 \, d}"," ",0,"1/2*(3*I*2^(2/3)*a*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(4/3*I*d*x + 4/3*I*c) + (-4*I*a^5/d^3)^(1/3)*(-I*sqrt(3)*d - d)*log(1/4*(4*2^(1/3)*a^3*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (I*sqrt(3)*d^2 - d^2)*(-4*I*a^5/d^3)^(2/3))/a^3) + (-4*I*a^5/d^3)^(1/3)*(I*sqrt(3)*d - d)*log(1/4*(4*2^(1/3)*a^3*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (-I*sqrt(3)*d^2 - d^2)*(-4*I*a^5/d^3)^(2/3))/a^3) + 2*(-4*I*a^5/d^3)^(1/3)*d*log(1/2*(2*2^(1/3)*a^3*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (-4*I*a^5/d^3)^(2/3)*d^2)/a^3))/d","B",0
288,0,0,0,0.482603," ","integrate(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2^{\frac{2}{3}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-\frac{2}{3} i \, d x - \frac{2}{3} i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*2^(2/3)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(e^(2*I*d*x + 2*I*c) + 1)*e^(-2/3*I*d*x - 2/3*I*c)/a, x)","F",0
289,0,0,0,0.534167," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} {\rm integral}\left(\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 30 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 8 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 11 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, e^{\left(i \, d x + i \, c\right)} - 4 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)}}{2 \, {\left(a d e^{\left(7 i \, d x + 7 i \, c\right)} - 6 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 11 \, a d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} - 12 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 8 \, a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}, x\right)}{a d e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)}}"," ",0,"(2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(3*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(4/3*I*d*x + 4/3*I*c) + (a*d*e^(4*I*d*x + 4*I*c) - 4*a*d*e^(3*I*d*x + 3*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c))*integral(1/2*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(6*I*d*x + 6*I*c) + 30*I*e^(5*I*d*x + 5*I*c) - 8*I*e^(4*I*d*x + 4*I*c) + 24*I*e^(3*I*d*x + 3*I*c) - 11*I*e^(2*I*d*x + 2*I*c) - 6*I*e^(I*d*x + I*c) - 4*I)*e^(4/3*I*d*x + 4/3*I*c)/(a*d*e^(7*I*d*x + 7*I*c) - 6*a*d*e^(6*I*d*x + 6*I*c) + 11*a*d*e^(5*I*d*x + 5*I*c) - 2*a*d*e^(4*I*d*x + 4*I*c) - 12*a*d*e^(3*I*d*x + 3*I*c) + 8*a*d*e^(2*I*d*x + 2*I*c)), x))/(a*d*e^(4*I*d*x + 4*I*c) - 4*a*d*e^(3*I*d*x + 3*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c))","F",0
290,1,478,0,0.442681," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(57 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 117 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 105 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 15 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 20 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(8 \, a d^{2} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 10 \, {\left({\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(-4 \, {\left(i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 10 \, {\left({\left(i \, \sqrt{3} a d + a d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, {\left(i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(i \, \sqrt{3} a d + a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(-4 \, {\left(-i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)}{20 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/20*(2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(57*I*e^(6*I*d*x + 6*I*c) + 117*I*e^(4*I*d*x + 4*I*c) + 105*I*e^(2*I*d*x + 2*I*c) + 15*I)*e^(4/3*I*d*x + 4/3*I*c) + 20*(a*d*e^(6*I*d*x + 6*I*c) + 2*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*(-1/16*I/(a*d^3))^(1/3)*log(8*a*d^2*(-1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 10*((-I*sqrt(3)*a*d + a*d)*e^(6*I*d*x + 6*I*c) + 2*(-I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (-I*sqrt(3)*a*d + a*d)*e^(2*I*d*x + 2*I*c))*(-1/16*I/(a*d^3))^(1/3)*log(-4*(I*sqrt(3)*a*d^2 + a*d^2)*(-1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 10*((I*sqrt(3)*a*d + a*d)*e^(6*I*d*x + 6*I*c) + 2*(I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (I*sqrt(3)*a*d + a*d)*e^(2*I*d*x + 2*I*c))*(-1/16*I/(a*d^3))^(1/3)*log(-4*(-I*sqrt(3)*a*d^2 + a*d^2)*(-1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))/(a*d*e^(6*I*d*x + 6*I*c) + 2*a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","B",0
291,1,418,0,0.439460," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{3 \cdot 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(7 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 20 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 10 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{1}{3}} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d^{2} \left(-\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 5 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(i \, \sqrt{3} a d + a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 5 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)}{20 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/20*(3*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(7*e^(4*I*d*x + 4*I*c) + 20*e^(2*I*d*x + 2*I*c) + 5)*e^(4/3*I*d*x + 4/3*I*c) + 10*(1/2)^(1/3)*(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*(-1/(a*d^3))^(1/3)*log(-2*(1/2)^(2/3)*a*d^2*(-1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 5*(1/2)^(1/3)*((I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (I*sqrt(3)*a*d + a*d)*e^(2*I*d*x + 2*I*c))*(-1/(a*d^3))^(1/3)*log(-(1/2)^(2/3)*(I*sqrt(3)*a*d^2 - a*d^2)*(-1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 5*(1/2)^(1/3)*((-I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (-I*sqrt(3)*a*d + a*d)*e^(2*I*d*x + 2*I*c))*(-1/(a*d^3))^(1/3)*log(-(1/2)^(2/3)*(-I*sqrt(3)*a*d^2 - a*d^2)*(-1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))/(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","B",0
292,1,314,0,0.430231," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{{\left(4 \, a d \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(8 \, a d^{2} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-9 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} - 2 \, {\left(-i \, \sqrt{3} a d + a d\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-4 \, {\left(i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left(i \, \sqrt{3} a d + a d\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-4 \, {\left(-i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(4*a*d*(1/16*I/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(8*a*d^2*(1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-9*I*e^(2*I*d*x + 2*I*c) - 3*I)*e^(4/3*I*d*x + 4/3*I*c) - 2*(-I*sqrt(3)*a*d + a*d)*(1/16*I/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-4*(I*sqrt(3)*a*d^2 + a*d^2)*(1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*(I*sqrt(3)*a*d + a*d)*(1/16*I/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-4*(-I*sqrt(3)*a*d^2 + a*d^2)*(1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
293,1,327,0,0.482930," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{{\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a d \left(\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d^{2} \left(\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a d + a d\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a d + a d\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 3 \cdot 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*(1/2)^(1/3)*a*d*(1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-2*(1/2)^(2/3)*a*d^2*(1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - (1/2)^(1/3)*(I*sqrt(3)*a*d + a*d)*(1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-(1/2)^(2/3)*(I*sqrt(3)*a*d^2 - a*d^2)*(1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - (1/2)^(1/3)*(-I*sqrt(3)*a*d + a*d)*(1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-(1/2)^(2/3)*(-I*sqrt(3)*a*d^2 - a*d^2)*(1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 3*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(e^(2*I*d*x + 2*I*c) + 1)*e^(4/3*I*d*x + 4/3*I*c))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
294,1,314,0,0.464735," ","integrate(1/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{{\left(4 \, a d \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(8 \, a d^{2} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} - 2 \, {\left(-i \, \sqrt{3} a d + a d\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-4 \, {\left(i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left(i \, \sqrt{3} a d + a d\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-4 \, {\left(-i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(-\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(4*a*d*(-1/16*I/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(8*a*d^2*(-1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(3*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(4/3*I*d*x + 4/3*I*c) - 2*(-I*sqrt(3)*a*d + a*d)*(-1/16*I/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-4*(I*sqrt(3)*a*d^2 + a*d^2)*(-1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*(I*sqrt(3)*a*d + a*d)*(-1/16*I/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-4*(-I*sqrt(3)*a*d^2 + a*d^2)*(-1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
295,1,580,0,0.450583," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{{\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a d \left(-\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d^{2} \left(-\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 4 \, a d \left(\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-a d^{2} \left(\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a d + a d\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a d + a d\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a d^{2} - a d^{2}\right)} \left(-\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 3 \cdot 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} - 2 \, {\left(-i \, \sqrt{3} a d + a d\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{1}{2} \, {\left(i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left(i \, \sqrt{3} a d + a d\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{1}{2} \, {\left(-i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{1}{a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*(1/2)^(1/3)*a*d*(-1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-2*(1/2)^(2/3)*a*d^2*(-1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 4*a*d*(1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-a*d^2*(1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - (1/2)^(1/3)*(I*sqrt(3)*a*d + a*d)*(-1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-(1/2)^(2/3)*(I*sqrt(3)*a*d^2 - a*d^2)*(-1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - (1/2)^(1/3)*(-I*sqrt(3)*a*d + a*d)*(-1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(-(1/2)^(2/3)*(-I*sqrt(3)*a*d^2 - a*d^2)*(-1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 3*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(e^(2*I*d*x + 2*I*c) + 1)*e^(4/3*I*d*x + 4/3*I*c) - 2*(-I*sqrt(3)*a*d + a*d)*(1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(1/2*(I*sqrt(3)*a*d^2 + a*d^2)*(1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*(I*sqrt(3)*a*d + a*d)*(1/(a*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(1/2*(-I*sqrt(3)*a*d^2 + a*d^2)*(1/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
296,1,717,0,0.476081," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-7 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 4 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} - a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(8 \, a d^{2} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 4 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} - a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(\frac{i}{27 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(9 \, a d^{2} \left(\frac{i}{27 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left({\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(i \, \sqrt{3} a d - a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(-4 \, {\left(i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left({\left(i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-i \, \sqrt{3} a d - a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(-4 \, {\left(-i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{i}{16 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left({\left(-i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(i \, \sqrt{3} a d - a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(\frac{i}{27 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(-\frac{9}{2} \, {\left(i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{i}{27 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 2 \, {\left({\left(i \, \sqrt{3} a d + a d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-i \, \sqrt{3} a d - a d\right)} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \left(\frac{i}{27 \, a d^{3}}\right)^{\frac{1}{3}} \log\left(-\frac{9}{2} \, {\left(-i \, \sqrt{3} a d^{2} + a d^{2}\right)} \left(\frac{i}{27 \, a d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)}{4 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} - a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/4*(2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-7*I*e^(4*I*d*x + 4*I*c) - 4*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(4/3*I*d*x + 4/3*I*c) + 4*(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*(1/16*I/(a*d^3))^(1/3)*log(8*a*d^2*(1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 4*(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))*(1/27*I/(a*d^3))^(1/3)*log(9*a*d^2*(1/27*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*((-I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (I*sqrt(3)*a*d - a*d)*e^(2*I*d*x + 2*I*c))*(1/16*I/(a*d^3))^(1/3)*log(-4*(I*sqrt(3)*a*d^2 + a*d^2)*(1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*((I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (-I*sqrt(3)*a*d - a*d)*e^(2*I*d*x + 2*I*c))*(1/16*I/(a*d^3))^(1/3)*log(-4*(-I*sqrt(3)*a*d^2 + a*d^2)*(1/16*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*((-I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (I*sqrt(3)*a*d - a*d)*e^(2*I*d*x + 2*I*c))*(1/27*I/(a*d^3))^(1/3)*log(-9/2*(I*sqrt(3)*a*d^2 + a*d^2)*(1/27*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 2*((I*sqrt(3)*a*d + a*d)*e^(4*I*d*x + 4*I*c) + (-I*sqrt(3)*a*d - a*d)*e^(2*I*d*x + 2*I*c))*(1/27*I/(a*d^3))^(1/3)*log(-9/2*(-I*sqrt(3)*a*d^2 + a*d^2)*(1/27*I/(a*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))/(a*d*e^(4*I*d*x + 4*I*c) - a*d*e^(2*I*d*x + 2*I*c))","B",0
297,1,305,0,0.439517," ","integrate(1/(a+I*a*tan(d*x+c))^(2/3),x, algorithm=""fricas"")","\frac{{\left(8 \, a d \left(-\frac{i}{32 \, a^{2} d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(4 i \, a d \left(-\frac{i}{32 \, a^{2} d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, {\left(-i \, \sqrt{3} a d + a d\right)} \left(-\frac{i}{32 \, a^{2} d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(2 \, \sqrt{3} a d + 2 i \, a d\right)} \left(-\frac{i}{32 \, a^{2} d^{3}}\right)^{\frac{1}{3}}\right) - 4 \, {\left(i \, \sqrt{3} a d + a d\right)} \left(-\frac{i}{32 \, a^{2} d^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(2 \, \sqrt{3} a d - 2 i \, a d\right)} \left(-\frac{i}{32 \, a^{2} d^{3}}\right)^{\frac{1}{3}}\right) + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a d}"," ",0,"1/8*(8*a*d*(-1/32*I/(a^2*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(4*I*a*d*(-1/32*I/(a^2*d^3))^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(-I*sqrt(3)*a*d + a*d)*(-1/32*I/(a^2*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (2*sqrt(3)*a*d + 2*I*a*d)*(-1/32*I/(a^2*d^3))^(1/3)) - 4*(I*sqrt(3)*a*d + a*d)*(-1/32*I/(a^2*d^3))^(1/3)*e^(2*I*d*x + 2*I*c)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (2*sqrt(3)*a*d - 2*I*a*d)*(-1/32*I/(a^2*d^3))^(1/3)) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(3*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(2/3*I*d*x + 2/3*I*c))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
298,0,0,0,0.465827," ","integrate(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2^{\frac{2}{3}} \left(\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-\frac{8}{3} i \, d x - \frac{8}{3} i \, c\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*2^(2/3)*((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))^m*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*e^(-8/3*I*d*x - 8/3*I*c)/a^2, x)","F",0
299,0,0,0,0.664883," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(15 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 12 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 42 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 24 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 39 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 12 i \, e^{\left(i \, d x + i \, c\right)} + 12 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 32 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - 4 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} {\rm integral}\left(\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-4 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 48 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 47 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 66 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 47 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 18 i \, e^{\left(i \, d x + i \, c\right)} - 4 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)}}{16 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - 6 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 11 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} - 12 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + 8 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}, x\right)}{32 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - 4 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + 4 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/32*(2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(15*I*e^(6*I*d*x + 6*I*c) - 12*I*e^(5*I*d*x + 5*I*c) + 42*I*e^(4*I*d*x + 4*I*c) - 24*I*e^(3*I*d*x + 3*I*c) + 39*I*e^(2*I*d*x + 2*I*c) - 12*I*e^(I*d*x + I*c) + 12*I)*e^(4/3*I*d*x + 4/3*I*c) + 32*(a^2*d*e^(6*I*d*x + 6*I*c) - 4*a^2*d*e^(5*I*d*x + 5*I*c) + 4*a^2*d*e^(4*I*d*x + 4*I*c))*integral(1/16*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-4*I*e^(6*I*d*x + 6*I*c) + 48*I*e^(5*I*d*x + 5*I*c) - 47*I*e^(4*I*d*x + 4*I*c) + 66*I*e^(3*I*d*x + 3*I*c) - 47*I*e^(2*I*d*x + 2*I*c) + 18*I*e^(I*d*x + I*c) - 4*I)*e^(4/3*I*d*x + 4/3*I*c)/(a^2*d*e^(7*I*d*x + 7*I*c) - 6*a^2*d*e^(6*I*d*x + 6*I*c) + 11*a^2*d*e^(5*I*d*x + 5*I*c) - 2*a^2*d*e^(4*I*d*x + 4*I*c) - 12*a^2*d*e^(3*I*d*x + 3*I*c) + 8*a^2*d*e^(2*I*d*x + 2*I*c)), x))/(a^2*d*e^(6*I*d*x + 6*I*c) - 4*a^2*d*e^(5*I*d*x + 5*I*c) + 4*a^2*d*e^(4*I*d*x + 4*I*c))","F",0
300,1,442,0,0.481631," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-693 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 1275 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 375 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 15 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 160 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(32 \, a^{3} d^{2} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 80 \, {\left({\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(-16 \, {\left(i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 80 \, {\left({\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(-16 \, {\left(-i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)}{160 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/160*(2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-693*I*e^(6*I*d*x + 6*I*c) - 1275*I*e^(4*I*d*x + 4*I*c) - 375*I*e^(2*I*d*x + 2*I*c) + 15*I)*e^(4/3*I*d*x + 4/3*I*c) + 160*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*(-1/128*I/(a^4*d^3))^(1/3)*log(32*a^3*d^2*(-1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 80*((-I*sqrt(3)*a^2*d + a^2*d)*e^(6*I*d*x + 6*I*c) + (-I*sqrt(3)*a^2*d + a^2*d)*e^(4*I*d*x + 4*I*c))*(-1/128*I/(a^4*d^3))^(1/3)*log(-16*(I*sqrt(3)*a^3*d^2 + a^3*d^2)*(-1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 80*((I*sqrt(3)*a^2*d + a^2*d)*e^(6*I*d*x + 6*I*c) + (I*sqrt(3)*a^2*d + a^2*d)*e^(4*I*d*x + 4*I*c))*(-1/128*I/(a^4*d^3))^(1/3)*log(-16*(-I*sqrt(3)*a^3*d^2 + a^3*d^2)*(-1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))/(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","B",0
301,1,366,0,0.444711," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{{\left(8 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a^{2} d \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{3} d^{2} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a^{3} d^{2} - a^{3} d^{2}\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a^{3} d^{2} - a^{3} d^{2}\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 3 \cdot 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(35 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 18 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(8*(1/2)^(1/3)*a^2*d*(-1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-2*(1/2)^(2/3)*a^3*d^2*(-1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(1/2)^(1/3)*(I*sqrt(3)*a^2*d + a^2*d)*(-1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-(1/2)^(2/3)*(I*sqrt(3)*a^3*d^2 - a^3*d^2)*(-1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(1/2)^(1/3)*(-I*sqrt(3)*a^2*d + a^2*d)*(-1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-(1/2)^(2/3)*(-I*sqrt(3)*a^3*d^2 - a^3*d^2)*(-1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 3*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(35*e^(4*I*d*x + 4*I*c) + 18*e^(2*I*d*x + 2*I*c) - 1)*e^(4/3*I*d*x + 4/3*I*c))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
302,1,345,0,0.458976," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{{\left(32 \, a^{2} d \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(32 \, a^{3} d^{2} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(33 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 30 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} - 16 \, {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-16 \, {\left(i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-16 \, {\left(-i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(32*a^2*d*(1/128*I/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(32*a^3*d^2*(1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(33*I*e^(4*I*d*x + 4*I*c) + 30*I*e^(2*I*d*x + 2*I*c) - 3*I)*e^(4/3*I*d*x + 4/3*I*c) - 16*(-I*sqrt(3)*a^2*d + a^2*d)*(1/128*I/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-16*(I*sqrt(3)*a^3*d^2 + a^3*d^2)*(1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*(I*sqrt(3)*a^2*d + a^2*d)*(1/128*I/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-16*(-I*sqrt(3)*a^3*d^2 + a^3*d^2)*(1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
303,1,360,0,0.446345," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{{\left(8 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a^{2} d \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{3} d^{2} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a^{3} d^{2} - a^{3} d^{2}\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a^{3} d^{2} - a^{3} d^{2}\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 3 \cdot 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(8*(1/2)^(1/3)*a^2*d*(1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-2*(1/2)^(2/3)*a^3*d^2*(1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(1/2)^(1/3)*(I*sqrt(3)*a^2*d + a^2*d)*(1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-(1/2)^(2/3)*(I*sqrt(3)*a^3*d^2 - a^3*d^2)*(1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(1/2)^(1/3)*(-I*sqrt(3)*a^2*d + a^2*d)*(1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-(1/2)^(2/3)*(-I*sqrt(3)*a^3*d^2 - a^3*d^2)*(1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 3*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(3*e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) - 1)*e^(4/3*I*d*x + 4/3*I*c))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
304,1,345,0,0.429772," ","integrate(1/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{{\left(32 \, a^{2} d \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(32 \, a^{3} d^{2} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 18 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} - 16 \, {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-16 \, {\left(i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-16 \, {\left(-i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(-\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(32*a^2*d*(-1/128*I/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(32*a^3*d^2*(-1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(15*I*e^(4*I*d*x + 4*I*c) + 18*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(4/3*I*d*x + 4/3*I*c) - 16*(-I*sqrt(3)*a^2*d + a^2*d)*(-1/128*I/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-16*(I*sqrt(3)*a^3*d^2 + a^3*d^2)*(-1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*(I*sqrt(3)*a^2*d + a^2*d)*(-1/128*I/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-16*(-I*sqrt(3)*a^3*d^2 + a^3*d^2)*(-1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
305,1,633,0,0.486938," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{{\left(8 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a^{2} d \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{3} d^{2} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 32 \, a^{2} d \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-a^{3} d^{2} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(i \, \sqrt{3} a^{3} d^{2} - a^{3} d^{2}\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(-i \, \sqrt{3} a^{3} d^{2} - a^{3} d^{2}\right)} \left(-\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 3 \cdot 2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(13 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 14 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} - 16 \, {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{1}{2} \, {\left(i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{1}{2} \, {\left(-i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{1}{a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{2} d}"," ",0,"1/32*(8*(1/2)^(1/3)*a^2*d*(-1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-2*(1/2)^(2/3)*a^3*d^2*(-1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 32*a^2*d*(1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-a^3*d^2*(1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(1/2)^(1/3)*(I*sqrt(3)*a^2*d + a^2*d)*(-1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-(1/2)^(2/3)*(I*sqrt(3)*a^3*d^2 - a^3*d^2)*(-1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 4*(1/2)^(1/3)*(-I*sqrt(3)*a^2*d + a^2*d)*(-1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(-(1/2)^(2/3)*(-I*sqrt(3)*a^3*d^2 - a^3*d^2)*(-1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 3*2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(13*e^(4*I*d*x + 4*I*c) + 14*e^(2*I*d*x + 2*I*c) + 1)*e^(4/3*I*d*x + 4/3*I*c) - 16*(-I*sqrt(3)*a^2*d + a^2*d)*(1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(1/2*(I*sqrt(3)*a^3*d^2 + a^3*d^2)*(1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*(I*sqrt(3)*a^2*d + a^2*d)*(1/(a^4*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(1/2*(-I*sqrt(3)*a^3*d^2 + a^3*d^2)*(1/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
306,1,792,0,0.481745," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-95 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 35 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 63 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 32 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(\frac{64 i}{27 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(\frac{9}{16} \, a^{3} d^{2} \left(\frac{64 i}{27 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) + 32 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(32 \, a^{3} d^{2} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left({\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(i \, \sqrt{3} a^{2} d - a^{2} d\right)} e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(\frac{64 i}{27 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(-\frac{9}{32} \, {\left(i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{64 i}{27 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left({\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-i \, \sqrt{3} a^{2} d - a^{2} d\right)} e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(\frac{64 i}{27 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(-\frac{9}{32} \, {\left(-i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{64 i}{27 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left({\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(i \, \sqrt{3} a^{2} d - a^{2} d\right)} e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(-16 \, {\left(i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 16 \, {\left({\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-i \, \sqrt{3} a^{2} d - a^{2} d\right)} e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{1}{3}} \log\left(-16 \, {\left(-i \, \sqrt{3} a^{3} d^{2} + a^{3} d^{2}\right)} \left(\frac{i}{128 \, a^{4} d^{3}}\right)^{\frac{2}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)}{32 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/32*(2^(2/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-95*I*e^(6*I*d*x + 6*I*c) - 35*I*e^(4*I*d*x + 4*I*c) + 63*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(4/3*I*d*x + 4/3*I*c) + 32*(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*(64/27*I/(a^4*d^3))^(1/3)*log(9/16*a^3*d^2*(64/27*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) + 32*(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*(1/128*I/(a^4*d^3))^(1/3)*log(32*a^3*d^2*(1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*((-I*sqrt(3)*a^2*d + a^2*d)*e^(6*I*d*x + 6*I*c) + (I*sqrt(3)*a^2*d - a^2*d)*e^(4*I*d*x + 4*I*c))*(64/27*I/(a^4*d^3))^(1/3)*log(-9/32*(I*sqrt(3)*a^3*d^2 + a^3*d^2)*(64/27*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*((I*sqrt(3)*a^2*d + a^2*d)*e^(6*I*d*x + 6*I*c) + (-I*sqrt(3)*a^2*d - a^2*d)*e^(4*I*d*x + 4*I*c))*(64/27*I/(a^4*d^3))^(1/3)*log(-9/32*(-I*sqrt(3)*a^3*d^2 + a^3*d^2)*(64/27*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*((-I*sqrt(3)*a^2*d + a^2*d)*e^(6*I*d*x + 6*I*c) + (I*sqrt(3)*a^2*d - a^2*d)*e^(4*I*d*x + 4*I*c))*(1/128*I/(a^4*d^3))^(1/3)*log(-16*(I*sqrt(3)*a^3*d^2 + a^3*d^2)*(1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 16*((I*sqrt(3)*a^2*d + a^2*d)*e^(6*I*d*x + 6*I*c) + (-I*sqrt(3)*a^2*d - a^2*d)*e^(4*I*d*x + 4*I*c))*(1/128*I/(a^4*d^3))^(1/3)*log(-16*(-I*sqrt(3)*a^3*d^2 + a^3*d^2)*(1/128*I/(a^4*d^3))^(2/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)))/(a^2*d*e^(6*I*d*x + 6*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))","B",0
307,1,336,0,0.501967," ","integrate(1/(a+I*a*tan(d*x+c))^(5/3),x, algorithm=""fricas"")","\frac{{\left(80 \, a^{2} d \left(-\frac{i}{256 \, a^{5} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(8 i \, a^{2} d \left(-\frac{i}{256 \, a^{5} d^{3}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right) - 40 \, {\left(-i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{i}{256 \, a^{5} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} - {\left(4 \, \sqrt{3} a^{2} d + 4 i \, a^{2} d\right)} \left(-\frac{i}{256 \, a^{5} d^{3}}\right)^{\frac{1}{3}}\right) - 40 \, {\left(i \, \sqrt{3} a^{2} d + a^{2} d\right)} \left(-\frac{i}{256 \, a^{5} d^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(4 \, \sqrt{3} a^{2} d - 4 i \, a^{2} d\right)} \left(-\frac{i}{256 \, a^{5} d^{3}}\right)^{\frac{1}{3}}\right) + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(21 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 27 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{80 \, a^{2} d}"," ",0,"1/80*(80*a^2*d*(-1/256*I/(a^5*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(8*I*a^2*d*(-1/256*I/(a^5*d^3))^(1/3) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c)) - 40*(-I*sqrt(3)*a^2*d + a^2*d)*(-1/256*I/(a^5*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) - (4*sqrt(3)*a^2*d + 4*I*a^2*d)*(-1/256*I/(a^5*d^3))^(1/3)) - 40*(I*sqrt(3)*a^2*d + a^2*d)*(-1/256*I/(a^5*d^3))^(1/3)*e^(4*I*d*x + 4*I*c)*log(2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(2/3*I*d*x + 2/3*I*c) + (4*sqrt(3)*a^2*d - 4*I*a^2*d)*(-1/256*I/(a^5*d^3))^(1/3)) + 2^(1/3)*(a/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(21*I*e^(4*I*d*x + 4*I*c) + 27*I*e^(2*I*d*x + 2*I*c) + 6*I)*e^(2/3*I*d*x + 2/3*I*c))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
308,0,0,0,0.442595," ","integrate((e*tan(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{-i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*a*((-I*e*e^(2*I*d*x + 2*I*c) + I*e)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
309,0,0,0,0.449899," ","integrate((e*tan(d*x+c))^m*(a-I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{-i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*a*((-I*e*e^(2*I*d*x + 2*I*c) + I*e)/(e^(2*I*d*x + 2*I*c) + 1))^m/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
310,0,0,0,0.531002," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{16 \, a^{4} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(8 i \, f x + 8 i \, e\right)}}{e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(16*a^4*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(8*I*f*x + 8*I*e)/(e^(8*I*f*x + 8*I*e) + 4*e^(6*I*f*x + 6*I*e) + 6*e^(4*I*f*x + 4*I*e) + 4*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
311,0,0,0,0.435111," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, a^{3} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(6 i \, f x + 6 i \, e\right)}}{e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(8*a^3*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(6*I*f*x + 6*I*e)/(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
312,0,0,0,0.515981," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, a^{2} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(4 i \, f x + 4 i \, e\right)}}{e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(4*a^2*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(4*I*f*x + 4*I*e)/(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
313,0,0,0,0.441319," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*a*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
314,0,0,0,0.471507," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(2*I*f*x + 2*I*e) + 1)*e^(-2*I*f*x - 2*I*e)/a, x)","F",0
315,0,0,0,0.619978," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)*e^(-4*I*f*x - 4*I*e)/a^2, x)","F",0
316,0,0,0,0.468744," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1)*e^(-6*I*f*x - 6*I*e)/a^3, x)","F",0
317,0,0,0,0.488958," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-8 i \, f x - 8 i \, e\right)}}{16 \, a^{4}}, x\right)"," ",0,"integral(1/16*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(8*I*f*x + 8*I*e) + 4*e^(6*I*f*x + 6*I*e) + 6*e^(4*I*f*x + 4*I*e) + 4*e^(2*I*f*x + 2*I*e) + 1)*e^(-8*I*f*x - 8*I*e)/a^4, x)","F",0
318,0,0,0,0.696057," ","integrate((d*tan(f*x+e))^n*(a-I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*a*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
319,0,0,0,0.424267," ","integrate((d*tan(f*x+e))^n/(a-I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(2*I*f*x + 2*I*e) + 1)/a, x)","F",0
320,0,0,0,0.522995," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \sqrt{2} a \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(3 i \, f x + 3 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*sqrt(2)*a*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*e^(3*I*f*x + 3*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
321,0,0,0,0.560755," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(i \, f x + i \, e\right)}, x\right)"," ",0,"integral(sqrt(2)*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*e^(I*f*x + I*e), x)","F",0
322,0,0,0,0.473017," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*sqrt(2)*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)*e^(-I*f*x - I*e)/a, x)","F",0
323,0,0,0,0.478696," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*sqrt(2)*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)*e^(-3*I*f*x - 3*I*e)/a^2, x)","F",0
324,0,0,0,0.439724," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n, x)","F",0
325,0,0,0,0.444909," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(e^{\left(8 i \, d x + 8 i \, c\right)} - 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(e^(8*I*d*x + 8*I*c) - 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) - 4*e^(2*I*d*x + 2*I*c) + 1)/(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
326,0,0,0,0.513954," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}}{e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(I*e^(6*I*d*x + 6*I*c) - 3*I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c) - I)/(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
327,0,0,0,0.434250," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(-(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) + 1)/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
328,0,0,0,0.461328," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
329,0,0,0,0.422428," ","integrate((a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m, x)","F",0
330,0,0,0,0.425340," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1), x)","F",0
331,0,0,0,0.482872," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(-(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)/(e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
332,0,0,0,0.461722," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
333,0,0,0,0.518558," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1)), x)","F",0
334,0,0,0,0.475959," ","integrate((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1), x)","F",0
335,0,0,0,0.467276," ","integrate((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(-(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt((-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1))*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)/(e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
336,1,227,0,0.710407," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} a d^{\frac{5}{2}} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, {\left(3 \, a d^{2} \tan\left(f x + e\right)^{2} + 5 \, a d^{2} \tan\left(f x + e\right) - 15 \, a d^{2}\right)} \sqrt{d \tan\left(f x + e\right)}}{30 \, f}, -\frac{15 \, \sqrt{2} a \sqrt{-d} d^{2} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) - 2 \, {\left(3 \, a d^{2} \tan\left(f x + e\right)^{2} + 5 \, a d^{2} \tan\left(f x + e\right) - 15 \, a d^{2}\right)} \sqrt{d \tan\left(f x + e\right)}}{15 \, f}\right]"," ",0,"[1/30*(15*sqrt(2)*a*d^(5/2)*log((d*tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 4*(3*a*d^2*tan(f*x + e)^2 + 5*a*d^2*tan(f*x + e) - 15*a*d^2)*sqrt(d*tan(f*x + e)))/f, -1/15*(15*sqrt(2)*a*sqrt(-d)*d^2*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e))) - 2*(3*a*d^2*tan(f*x + e)^2 + 5*a*d^2*tan(f*x + e) - 15*a*d^2)*sqrt(d*tan(f*x + e)))/f]","A",0
337,1,184,0,0.425581," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} a \sqrt{-d} d \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) - 1\right)} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, {\left(a d \tan\left(f x + e\right) + 3 \, a d\right)} \sqrt{d \tan\left(f x + e\right)}}{6 \, f}, -\frac{3 \, \sqrt{2} a d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) - 2 \, {\left(a d \tan\left(f x + e\right) + 3 \, a d\right)} \sqrt{d \tan\left(f x + e\right)}}{3 \, f}\right]"," ",0,"[1/6*(3*sqrt(2)*a*sqrt(-d)*d*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) - 1) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 4*(a*d*tan(f*x + e) + 3*a*d)*sqrt(d*tan(f*x + e)))/f, -1/3*(3*sqrt(2)*a*d^(3/2)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e))) - 2*(a*d*tan(f*x + e) + 3*a*d)*sqrt(d*tan(f*x + e)))/f]","A",0
338,1,157,0,0.416158," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, \sqrt{d \tan\left(f x + e\right)} a}{2 \, f}, \frac{\sqrt{2} a \sqrt{-d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} a}{f}\right]"," ",0,"[1/2*(sqrt(2)*a*sqrt(d)*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 4*sqrt(d*tan(f*x + e))*a)/f, (sqrt(2)*a*sqrt(-d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e))) + 2*sqrt(d*tan(f*x + e))*a)/f]","A",0
339,1,125,0,0.482094," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{1}{d}} \log\left(\frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) - 1\right)} + \tan\left(f x + e\right)^{2} - 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, f}, \frac{\sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right)}{\sqrt{d} f}\right]"," ",0,"[1/2*sqrt(2)*a*sqrt(-1/d)*log((2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) - 1) + tan(f*x + e)^2 - 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1))/f, sqrt(2)*a*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e)))/(sqrt(d)*f)]","A",0
340,1,191,0,0.444826," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{d} \log\left(\frac{\tan\left(f x + e\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) + 1\right)}}{\sqrt{d}} + 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right) - 4 \, \sqrt{d \tan\left(f x + e\right)} a}{2 \, d^{2} f \tan\left(f x + e\right)}, -\frac{\sqrt{2} a d \sqrt{-\frac{1}{d}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, \tan\left(f x + e\right)}\right) \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} a}{d^{2} f \tan\left(f x + e\right)}\right]"," ",0,"[1/2*(sqrt(2)*a*sqrt(d)*log((tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) + 1)/sqrt(d) + 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e) - 4*sqrt(d*tan(f*x + e))*a)/(d^2*f*tan(f*x + e)), -(sqrt(2)*a*d*sqrt(-1/d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) + 1)/tan(f*x + e))*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*a)/(d^2*f*tan(f*x + e))]","A",0
341,1,220,0,0.453290," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} a d \sqrt{-\frac{1}{d}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) - 1\right)} - \tan\left(f x + e\right)^{2} + 4 \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right)^{2} - 4 \, {\left(3 \, a \tan\left(f x + e\right) + a\right)} \sqrt{d \tan\left(f x + e\right)}}{6 \, d^{3} f \tan\left(f x + e\right)^{2}}, -\frac{3 \, \sqrt{2} a \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) \tan\left(f x + e\right)^{2} + 2 \, {\left(3 \, a \tan\left(f x + e\right) + a\right)} \sqrt{d \tan\left(f x + e\right)}}{3 \, d^{3} f \tan\left(f x + e\right)^{2}}\right]"," ",0,"[1/6*(3*sqrt(2)*a*d*sqrt(-1/d)*log(-(2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) - 1) - tan(f*x + e)^2 + 4*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e)^2 - 4*(3*a*tan(f*x + e) + a)*sqrt(d*tan(f*x + e)))/(d^3*f*tan(f*x + e)^2), -1/3*(3*sqrt(2)*a*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e)))*tan(f*x + e)^2 + 2*(3*a*tan(f*x + e) + a)*sqrt(d*tan(f*x + e)))/(d^3*f*tan(f*x + e)^2)]","A",0
342,1,243,0,0.446396," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} a \sqrt{d} \log\left(\frac{\tan\left(f x + e\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) + 1\right)}}{\sqrt{d}} + 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right)^{3} + 4 \, {\left(15 \, a \tan\left(f x + e\right)^{2} - 5 \, a \tan\left(f x + e\right) - 3 \, a\right)} \sqrt{d \tan\left(f x + e\right)}}{30 \, d^{4} f \tan\left(f x + e\right)^{3}}, \frac{15 \, \sqrt{2} a d \sqrt{-\frac{1}{d}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, \tan\left(f x + e\right)}\right) \tan\left(f x + e\right)^{3} + 2 \, {\left(15 \, a \tan\left(f x + e\right)^{2} - 5 \, a \tan\left(f x + e\right) - 3 \, a\right)} \sqrt{d \tan\left(f x + e\right)}}{15 \, d^{4} f \tan\left(f x + e\right)^{3}}\right]"," ",0,"[1/30*(15*sqrt(2)*a*sqrt(d)*log((tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) + 1)/sqrt(d) + 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e)^3 + 4*(15*a*tan(f*x + e)^2 - 5*a*tan(f*x + e) - 3*a)*sqrt(d*tan(f*x + e)))/(d^4*f*tan(f*x + e)^3), 1/15*(15*sqrt(2)*a*d*sqrt(-1/d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) + 1)/tan(f*x + e))*tan(f*x + e)^3 + 2*(15*a*tan(f*x + e)^2 - 5*a*tan(f*x + e) - 3*a)*sqrt(d*tan(f*x + e)))/(d^4*f*tan(f*x + e)^3)]","A",0
343,1,736,0,0.456928," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{140 \, \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{a^{8} d^{10} + \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{3}{4}} a^{2} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{\frac{a^{4} d^{5} \sin\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{10}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8} d^{10}}\right) \cos\left(f x + e\right)^{3} + 140 \, \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(\frac{a^{8} d^{10} - \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{3}{4}} a^{2} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{\frac{a^{4} d^{5} \sin\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{10}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8} d^{10}}\right) \cos\left(f x + e\right)^{3} - 35 \, \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{3} \log\left(\frac{a^{4} d^{5} \sin\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{10}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 35 \, \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{3} \log\left(\frac{a^{4} d^{5} \sin\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8} d^{10}}{f^{4}}\right)^{\frac{1}{4}} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{10}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(84 \, a^{2} d^{2} \cos\left(f x + e\right)^{3} - 14 \, a^{2} d^{2} \cos\left(f x + e\right) + 5 \, {\left(a^{2} d^{2} \cos\left(f x + e\right)^{2} - a^{2} d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{70 \, f \cos\left(f x + e\right)^{3}}"," ",0,"-1/70*(140*sqrt(2)*(a^8*d^10/f^4)^(1/4)*f*arctan(-(a^8*d^10 + sqrt(2)*(a^8*d^10/f^4)^(3/4)*a^2*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e)) - sqrt(2)*(a^8*d^10/f^4)^(3/4)*f^3*sqrt((a^4*d^5*sin(f*x + e) + sqrt(2)*(a^8*d^10/f^4)^(1/4)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^10/f^4)*f^2*cos(f*x + e))/cos(f*x + e)))/(a^8*d^10))*cos(f*x + e)^3 + 140*sqrt(2)*(a^8*d^10/f^4)^(1/4)*f*arctan((a^8*d^10 - sqrt(2)*(a^8*d^10/f^4)^(3/4)*a^2*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e)) + sqrt(2)*(a^8*d^10/f^4)^(3/4)*f^3*sqrt((a^4*d^5*sin(f*x + e) - sqrt(2)*(a^8*d^10/f^4)^(1/4)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^10/f^4)*f^2*cos(f*x + e))/cos(f*x + e)))/(a^8*d^10))*cos(f*x + e)^3 - 35*sqrt(2)*(a^8*d^10/f^4)^(1/4)*f*cos(f*x + e)^3*log((a^4*d^5*sin(f*x + e) + sqrt(2)*(a^8*d^10/f^4)^(1/4)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^10/f^4)*f^2*cos(f*x + e))/cos(f*x + e)) + 35*sqrt(2)*(a^8*d^10/f^4)^(1/4)*f*cos(f*x + e)^3*log((a^4*d^5*sin(f*x + e) - sqrt(2)*(a^8*d^10/f^4)^(1/4)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^10/f^4)*f^2*cos(f*x + e))/cos(f*x + e)) + 4*(84*a^2*d^2*cos(f*x + e)^3 - 14*a^2*d^2*cos(f*x + e) + 5*(a^2*d^2*cos(f*x + e)^2 - a^2*d^2)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(f*cos(f*x + e)^3)","B",0
344,1,736,0,0.496847," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{60 \, \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{a^{8} d^{6} + \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} a^{6} d^{4} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{a^{12} d^{9} \sin\left(f x + e\right) + \sqrt{\frac{a^{8} d^{6}}{f^{4}}} a^{8} d^{6} f^{2} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{3}{4}} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8} d^{6}}\right) \cos\left(f x + e\right)^{2} + 60 \, \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(\frac{a^{8} d^{6} - \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} a^{6} d^{4} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{a^{12} d^{9} \sin\left(f x + e\right) + \sqrt{\frac{a^{8} d^{6}}{f^{4}}} a^{8} d^{6} f^{2} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{3}{4}} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8} d^{6}}\right) \cos\left(f x + e\right)^{2} + 15 \, \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{2} \log\left(\frac{a^{12} d^{9} \sin\left(f x + e\right) + \sqrt{\frac{a^{8} d^{6}}{f^{4}}} a^{8} d^{6} f^{2} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{3}{4}} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 15 \, \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{2} \log\left(\frac{a^{12} d^{9} \sin\left(f x + e\right) + \sqrt{\frac{a^{8} d^{6}}{f^{4}}} a^{8} d^{6} f^{2} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8} d^{6}}{f^{4}}\right)^{\frac{3}{4}} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(3 \, a^{2} d \cos\left(f x + e\right)^{2} - 10 \, a^{2} d \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a^{2} d\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{30 \, f \cos\left(f x + e\right)^{2}}"," ",0,"1/30*(60*sqrt(2)*(a^8*d^6/f^4)^(1/4)*f*arctan(-(a^8*d^6 + sqrt(2)*(a^8*d^6/f^4)^(1/4)*a^6*d^4*f*sqrt(d*sin(f*x + e)/cos(f*x + e)) - sqrt(2)*(a^8*d^6/f^4)^(1/4)*f*sqrt((a^12*d^9*sin(f*x + e) + sqrt(a^8*d^6/f^4)*a^8*d^6*f^2*cos(f*x + e) + sqrt(2)*(a^8*d^6/f^4)^(3/4)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)))/(a^8*d^6))*cos(f*x + e)^2 + 60*sqrt(2)*(a^8*d^6/f^4)^(1/4)*f*arctan((a^8*d^6 - sqrt(2)*(a^8*d^6/f^4)^(1/4)*a^6*d^4*f*sqrt(d*sin(f*x + e)/cos(f*x + e)) + sqrt(2)*(a^8*d^6/f^4)^(1/4)*f*sqrt((a^12*d^9*sin(f*x + e) + sqrt(a^8*d^6/f^4)*a^8*d^6*f^2*cos(f*x + e) - sqrt(2)*(a^8*d^6/f^4)^(3/4)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)))/(a^8*d^6))*cos(f*x + e)^2 + 15*sqrt(2)*(a^8*d^6/f^4)^(1/4)*f*cos(f*x + e)^2*log((a^12*d^9*sin(f*x + e) + sqrt(a^8*d^6/f^4)*a^8*d^6*f^2*cos(f*x + e) + sqrt(2)*(a^8*d^6/f^4)^(3/4)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)) - 15*sqrt(2)*(a^8*d^6/f^4)^(1/4)*f*cos(f*x + e)^2*log((a^12*d^9*sin(f*x + e) + sqrt(a^8*d^6/f^4)*a^8*d^6*f^2*cos(f*x + e) - sqrt(2)*(a^8*d^6/f^4)^(3/4)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)) - 4*(3*a^2*d*cos(f*x + e)^2 - 10*a^2*d*cos(f*x + e)*sin(f*x + e) - 3*a^2*d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(f*cos(f*x + e)^2)","B",0
345,1,661,0,0.593724," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{a^{8} d^{2} + \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{3}{4}} a^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{\frac{a^{4} d \sin\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{2}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8} d^{2}}\right) \cos\left(f x + e\right) + 12 \, \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(\frac{a^{8} d^{2} - \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{3}{4}} a^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{\frac{a^{4} d \sin\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{2}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8} d^{2}}\right) \cos\left(f x + e\right) - 3 \, \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right) \log\left(\frac{a^{4} d \sin\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{2}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 3 \, \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right) \log\left(\frac{a^{4} d \sin\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8} d^{2}}{f^{4}}\right)^{\frac{1}{4}} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8} d^{2}}{f^{4}}} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(6 \, a^{2} \cos\left(f x + e\right) + a^{2} \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{6 \, f \cos\left(f x + e\right)}"," ",0,"1/6*(12*sqrt(2)*(a^8*d^2/f^4)^(1/4)*f*arctan(-(a^8*d^2 + sqrt(2)*(a^8*d^2/f^4)^(3/4)*a^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e)) - sqrt(2)*(a^8*d^2/f^4)^(3/4)*f^3*sqrt((a^4*d*sin(f*x + e) + sqrt(2)*(a^8*d^2/f^4)^(1/4)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^2/f^4)*f^2*cos(f*x + e))/cos(f*x + e)))/(a^8*d^2))*cos(f*x + e) + 12*sqrt(2)*(a^8*d^2/f^4)^(1/4)*f*arctan((a^8*d^2 - sqrt(2)*(a^8*d^2/f^4)^(3/4)*a^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e)) + sqrt(2)*(a^8*d^2/f^4)^(3/4)*f^3*sqrt((a^4*d*sin(f*x + e) - sqrt(2)*(a^8*d^2/f^4)^(1/4)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^2/f^4)*f^2*cos(f*x + e))/cos(f*x + e)))/(a^8*d^2))*cos(f*x + e) - 3*sqrt(2)*(a^8*d^2/f^4)^(1/4)*f*cos(f*x + e)*log((a^4*d*sin(f*x + e) + sqrt(2)*(a^8*d^2/f^4)^(1/4)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^2/f^4)*f^2*cos(f*x + e))/cos(f*x + e)) + 3*sqrt(2)*(a^8*d^2/f^4)^(1/4)*f*cos(f*x + e)*log((a^4*d*sin(f*x + e) - sqrt(2)*(a^8*d^2/f^4)^(1/4)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8*d^2/f^4)*f^2*cos(f*x + e))/cos(f*x + e)) + 4*(6*a^2*cos(f*x + e) + a^2*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(f*cos(f*x + e))","B",0
346,1,641,0,0.476585," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} d f \arctan\left(-\frac{\sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} a^{6} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + a^{8} - \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{a^{12} d \sin\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{3}{4}} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8}}{d^{2} f^{4}}} a^{8} d^{2} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8}}\right) + 4 \, \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} d f \arctan\left(-\frac{\sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} a^{6} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - a^{8} - \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{a^{12} d \sin\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{3}{4}} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8}}{d^{2} f^{4}}} a^{8} d^{2} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a^{8}}\right) + \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} d f \log\left(\frac{a^{12} d \sin\left(f x + e\right) + \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{3}{4}} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8}}{d^{2} f^{4}}} a^{8} d^{2} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{1}{4}} d f \log\left(\frac{a^{12} d \sin\left(f x + e\right) - \sqrt{2} \left(\frac{a^{8}}{d^{2} f^{4}}\right)^{\frac{3}{4}} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + \sqrt{\frac{a^{8}}{d^{2} f^{4}}} a^{8} d^{2} f^{2} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, a^{2} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, d f}"," ",0,"-1/2*(4*sqrt(2)*(a^8/(d^2*f^4))^(1/4)*d*f*arctan(-(sqrt(2)*(a^8/(d^2*f^4))^(1/4)*a^6*f*sqrt(d*sin(f*x + e)/cos(f*x + e)) + a^8 - sqrt(2)*(a^8/(d^2*f^4))^(1/4)*f*sqrt((a^12*d*sin(f*x + e) + sqrt(2)*(a^8/(d^2*f^4))^(3/4)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8/(d^2*f^4))*a^8*d^2*f^2*cos(f*x + e))/cos(f*x + e)))/a^8) + 4*sqrt(2)*(a^8/(d^2*f^4))^(1/4)*d*f*arctan(-(sqrt(2)*(a^8/(d^2*f^4))^(1/4)*a^6*f*sqrt(d*sin(f*x + e)/cos(f*x + e)) - a^8 - sqrt(2)*(a^8/(d^2*f^4))^(1/4)*f*sqrt((a^12*d*sin(f*x + e) - sqrt(2)*(a^8/(d^2*f^4))^(3/4)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8/(d^2*f^4))*a^8*d^2*f^2*cos(f*x + e))/cos(f*x + e)))/a^8) + sqrt(2)*(a^8/(d^2*f^4))^(1/4)*d*f*log((a^12*d*sin(f*x + e) + sqrt(2)*(a^8/(d^2*f^4))^(3/4)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8/(d^2*f^4))*a^8*d^2*f^2*cos(f*x + e))/cos(f*x + e)) - sqrt(2)*(a^8/(d^2*f^4))^(1/4)*d*f*log((a^12*d*sin(f*x + e) - sqrt(2)*(a^8/(d^2*f^4))^(3/4)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e) + sqrt(a^8/(d^2*f^4))*a^8*d^2*f^2*cos(f*x + e))/cos(f*x + e)) - 4*a^2*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(d*f)","B",0
347,1,753,0,0.476780," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{4 \, a^{2} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 4 \, {\left(\sqrt{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{2} f\right)} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{2} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{4} f^{3} \sqrt{\frac{d^{4} f^{2} \sqrt{\frac{a^{8}}{d^{6} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + a^{4} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{3}{4}} + a^{8}}{a^{8}}\right) - 4 \, {\left(\sqrt{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{2} f\right)} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{2} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{4} f^{3} \sqrt{\frac{d^{4} f^{2} \sqrt{\frac{a^{8}}{d^{6} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + a^{4} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{3}{4}} - a^{8}}{a^{8}}\right) + {\left(\sqrt{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{2} f\right)} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{d^{4} f^{2} \sqrt{\frac{a^{8}}{d^{6} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + a^{4} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - {\left(\sqrt{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{2} f\right)} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{d^{4} f^{2} \sqrt{\frac{a^{8}}{d^{6} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + a^{4} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)}{2 \, {\left(d^{2} f \cos\left(f x + e\right)^{2} - d^{2} f\right)}}"," ",0,"1/2*(4*a^2*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 4*(sqrt(2)*d^2*f*cos(f*x + e)^2 - sqrt(2)*d^2*f)*(a^8/(d^6*f^4))^(1/4)*arctan(-(sqrt(2)*a^2*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^6*f^4))^(3/4) - sqrt(2)*d^4*f^3*sqrt((d^4*f^2*sqrt(a^8/(d^6*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^6*f^4))^(1/4)*cos(f*x + e) + a^4*d*sin(f*x + e))/cos(f*x + e))*(a^8/(d^6*f^4))^(3/4) + a^8)/a^8) - 4*(sqrt(2)*d^2*f*cos(f*x + e)^2 - sqrt(2)*d^2*f)*(a^8/(d^6*f^4))^(1/4)*arctan(-(sqrt(2)*a^2*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^6*f^4))^(3/4) - sqrt(2)*d^4*f^3*sqrt((d^4*f^2*sqrt(a^8/(d^6*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^6*f^4))^(1/4)*cos(f*x + e) + a^4*d*sin(f*x + e))/cos(f*x + e))*(a^8/(d^6*f^4))^(3/4) - a^8)/a^8) + (sqrt(2)*d^2*f*cos(f*x + e)^2 - sqrt(2)*d^2*f)*(a^8/(d^6*f^4))^(1/4)*log((d^4*f^2*sqrt(a^8/(d^6*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^6*f^4))^(1/4)*cos(f*x + e) + a^4*d*sin(f*x + e))/cos(f*x + e)) - (sqrt(2)*d^2*f*cos(f*x + e)^2 - sqrt(2)*d^2*f)*(a^8/(d^6*f^4))^(1/4)*log((d^4*f^2*sqrt(a^8/(d^6*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^6*f^4))^(1/4)*cos(f*x + e) + a^4*d*sin(f*x + e))/cos(f*x + e)))/(d^2*f*cos(f*x + e)^2 - d^2*f)","B",0
348,1,785,0,0.506591," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{12 \, {\left(\sqrt{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{3} f\right)} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}} + a^{8} - \sqrt{2} d^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{8} d^{6} f^{2} \sqrt{\frac{a^{8}}{d^{10} f^{4}}} \cos\left(f x + e\right) + a^{12} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}}}{a^{8}}\right) + 12 \, {\left(\sqrt{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{3} f\right)} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}} - a^{8} - \sqrt{2} d^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{8} d^{6} f^{2} \sqrt{\frac{a^{8}}{d^{10} f^{4}}} \cos\left(f x + e\right) - a^{12} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}}}{a^{8}}\right) + 3 \, {\left(\sqrt{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{3} f\right)} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{8} d^{6} f^{2} \sqrt{\frac{a^{8}}{d^{10} f^{4}}} \cos\left(f x + e\right) + a^{12} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 3 \, {\left(\sqrt{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} d^{3} f\right)} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8}}{d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{8} d^{6} f^{2} \sqrt{\frac{a^{8}}{d^{10} f^{4}}} \cos\left(f x + e\right) - a^{12} d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(a^{2} \cos\left(f x + e\right)^{2} + 6 \, a^{2} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{6 \, {\left(d^{3} f \cos\left(f x + e\right)^{2} - d^{3} f\right)}}"," ",0,"1/6*(12*(sqrt(2)*d^3*f*cos(f*x + e)^2 - sqrt(2)*d^3*f)*(a^8/(d^10*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^10*f^4))^(1/4) + a^8 - sqrt(2)*d^2*f*sqrt((sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^10*f^4))^(3/4)*cos(f*x + e) + a^8*d^6*f^2*sqrt(a^8/(d^10*f^4))*cos(f*x + e) + a^12*d*sin(f*x + e))/cos(f*x + e))*(a^8/(d^10*f^4))^(1/4))/a^8) + 12*(sqrt(2)*d^3*f*cos(f*x + e)^2 - sqrt(2)*d^3*f)*(a^8/(d^10*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^10*f^4))^(1/4) - a^8 - sqrt(2)*d^2*f*sqrt(-(sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^10*f^4))^(3/4)*cos(f*x + e) - a^8*d^6*f^2*sqrt(a^8/(d^10*f^4))*cos(f*x + e) - a^12*d*sin(f*x + e))/cos(f*x + e))*(a^8/(d^10*f^4))^(1/4))/a^8) + 3*(sqrt(2)*d^3*f*cos(f*x + e)^2 - sqrt(2)*d^3*f)*(a^8/(d^10*f^4))^(1/4)*log((sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^10*f^4))^(3/4)*cos(f*x + e) + a^8*d^6*f^2*sqrt(a^8/(d^10*f^4))*cos(f*x + e) + a^12*d*sin(f*x + e))/cos(f*x + e)) - 3*(sqrt(2)*d^3*f*cos(f*x + e)^2 - sqrt(2)*d^3*f)*(a^8/(d^10*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(a^8/(d^10*f^4))^(3/4)*cos(f*x + e) - a^8*d^6*f^2*sqrt(a^8/(d^10*f^4))*cos(f*x + e) - a^12*d*sin(f*x + e))/cos(f*x + e)) + 4*(a^2*cos(f*x + e)^2 + 6*a^2*cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(d^3*f*cos(f*x + e)^2 - d^3*f)","B",0
349,1,338,0,0.496394," ","integrate((d*tan(f*x+e))^(7/2)*(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{1155 \, \sqrt{2} a^{3} d^{\frac{7}{2}} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(105 \, a^{3} d^{3} \tan\left(f x + e\right)^{5} + 385 \, a^{3} d^{3} \tan\left(f x + e\right)^{4} + 330 \, a^{3} d^{3} \tan\left(f x + e\right)^{3} - 462 \, a^{3} d^{3} \tan\left(f x + e\right)^{2} - 770 \, a^{3} d^{3} \tan\left(f x + e\right) + 2310 \, a^{3} d^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{1155 \, f}, \frac{2 \, {\left(1155 \, \sqrt{2} a^{3} \sqrt{-d} d^{3} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) + {\left(105 \, a^{3} d^{3} \tan\left(f x + e\right)^{5} + 385 \, a^{3} d^{3} \tan\left(f x + e\right)^{4} + 330 \, a^{3} d^{3} \tan\left(f x + e\right)^{3} - 462 \, a^{3} d^{3} \tan\left(f x + e\right)^{2} - 770 \, a^{3} d^{3} \tan\left(f x + e\right) + 2310 \, a^{3} d^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{1155 \, f}\right]"," ",0,"[1/1155*(1155*sqrt(2)*a^3*d^(7/2)*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 2*(105*a^3*d^3*tan(f*x + e)^5 + 385*a^3*d^3*tan(f*x + e)^4 + 330*a^3*d^3*tan(f*x + e)^3 - 462*a^3*d^3*tan(f*x + e)^2 - 770*a^3*d^3*tan(f*x + e) + 2310*a^3*d^3)*sqrt(d*tan(f*x + e)))/f, 2/1155*(1155*sqrt(2)*a^3*sqrt(-d)*d^3*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e))) + (105*a^3*d^3*tan(f*x + e)^5 + 385*a^3*d^3*tan(f*x + e)^4 + 330*a^3*d^3*tan(f*x + e)^3 - 462*a^3*d^3*tan(f*x + e)^2 - 770*a^3*d^3*tan(f*x + e) + 2310*a^3*d^3)*sqrt(d*tan(f*x + e)))/f]","A",0
350,1,303,0,0.523475," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{2} a^{3} \sqrt{-d} d^{2} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) - 1\right)} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(35 \, a^{3} d^{2} \tan\left(f x + e\right)^{4} + 135 \, a^{3} d^{2} \tan\left(f x + e\right)^{3} + 126 \, a^{3} d^{2} \tan\left(f x + e\right)^{2} - 210 \, a^{3} d^{2} \tan\left(f x + e\right) - 630 \, a^{3} d^{2}\right)} \sqrt{d \tan\left(f x + e\right)}}{315 \, f}, \frac{2 \, {\left(315 \, \sqrt{2} a^{3} d^{\frac{5}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) + {\left(35 \, a^{3} d^{2} \tan\left(f x + e\right)^{4} + 135 \, a^{3} d^{2} \tan\left(f x + e\right)^{3} + 126 \, a^{3} d^{2} \tan\left(f x + e\right)^{2} - 210 \, a^{3} d^{2} \tan\left(f x + e\right) - 630 \, a^{3} d^{2}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{315 \, f}\right]"," ",0,"[1/315*(315*sqrt(2)*a^3*sqrt(-d)*d^2*log((d*tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) - 1) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 2*(35*a^3*d^2*tan(f*x + e)^4 + 135*a^3*d^2*tan(f*x + e)^3 + 126*a^3*d^2*tan(f*x + e)^2 - 210*a^3*d^2*tan(f*x + e) - 630*a^3*d^2)*sqrt(d*tan(f*x + e)))/f, 2/315*(315*sqrt(2)*a^3*d^(5/2)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e))) + (35*a^3*d^2*tan(f*x + e)^4 + 135*a^3*d^2*tan(f*x + e)^3 + 126*a^3*d^2*tan(f*x + e)^2 - 210*a^3*d^2*tan(f*x + e) - 630*a^3*d^2)*sqrt(d*tan(f*x + e)))/f]","A",0
351,1,257,0,0.483892," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{2} a^{3} d^{\frac{3}{2}} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(15 \, a^{3} d \tan\left(f x + e\right)^{3} + 63 \, a^{3} d \tan\left(f x + e\right)^{2} + 70 \, a^{3} d \tan\left(f x + e\right) - 210 \, a^{3} d\right)} \sqrt{d \tan\left(f x + e\right)}}{105 \, f}, -\frac{2 \, {\left(105 \, \sqrt{2} a^{3} \sqrt{-d} d \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) - {\left(15 \, a^{3} d \tan\left(f x + e\right)^{3} + 63 \, a^{3} d \tan\left(f x + e\right)^{2} + 70 \, a^{3} d \tan\left(f x + e\right) - 210 \, a^{3} d\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{105 \, f}\right]"," ",0,"[1/105*(105*sqrt(2)*a^3*d^(3/2)*log((d*tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 2*(15*a^3*d*tan(f*x + e)^3 + 63*a^3*d*tan(f*x + e)^2 + 70*a^3*d*tan(f*x + e) - 210*a^3*d)*sqrt(d*tan(f*x + e)))/f, -2/105*(105*sqrt(2)*a^3*sqrt(-d)*d*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e))) - (15*a^3*d*tan(f*x + e)^3 + 63*a^3*d*tan(f*x + e)^2 + 70*a^3*d*tan(f*x + e) - 210*a^3*d)*sqrt(d*tan(f*x + e)))/f]","A",0
352,1,217,0,0.589791," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} a^{3} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) - 1\right)} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(a^{3} \tan\left(f x + e\right)^{2} + 5 \, a^{3} \tan\left(f x + e\right) + 10 \, a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{5 \, f}, -\frac{2 \, {\left(5 \, \sqrt{2} a^{3} \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) - {\left(a^{3} \tan\left(f x + e\right)^{2} + 5 \, a^{3} \tan\left(f x + e\right) + 10 \, a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{5 \, f}\right]"," ",0,"[1/5*(5*sqrt(2)*a^3*sqrt(-d)*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) - 1) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 2*(a^3*tan(f*x + e)^2 + 5*a^3*tan(f*x + e) + 10*a^3)*sqrt(d*tan(f*x + e)))/f, -2/5*(5*sqrt(2)*a^3*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e))) - (a^3*tan(f*x + e)^2 + 5*a^3*tan(f*x + e) + 10*a^3)*sqrt(d*tan(f*x + e)))/f]","A",0
353,1,198,0,0.458049," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} a^{3} \sqrt{d} \log\left(\frac{\tan\left(f x + e\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) + 1\right)}}{\sqrt{d}} + 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(a^{3} \tan\left(f x + e\right) + 9 \, a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{3 \, d f}, \frac{2 \, {\left(3 \, \sqrt{2} a^{3} d \sqrt{-\frac{1}{d}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, \tan\left(f x + e\right)}\right) + {\left(a^{3} \tan\left(f x + e\right) + 9 \, a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{3 \, d f}\right]"," ",0,"[1/3*(3*sqrt(2)*a^3*sqrt(d)*log((tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) + 1)/sqrt(d) + 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1)) + 2*(a^3*tan(f*x + e) + 9*a^3)*sqrt(d*tan(f*x + e)))/(d*f), 2/3*(3*sqrt(2)*a^3*d*sqrt(-1/d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) + 1)/tan(f*x + e)) + (a^3*tan(f*x + e) + 9*a^3)*sqrt(d*tan(f*x + e)))/(d*f)]","A",0
354,1,223,0,0.556643," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a^{3} d \sqrt{-\frac{1}{d}} \log\left(\frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) - 1\right)} + \tan\left(f x + e\right)^{2} - 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right) + 2 \, {\left(a^{3} \tan\left(f x + e\right) - a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{d^{2} f \tan\left(f x + e\right)}, \frac{2 \, {\left(\sqrt{2} a^{3} \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) \tan\left(f x + e\right) + {\left(a^{3} \tan\left(f x + e\right) - a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{d^{2} f \tan\left(f x + e\right)}\right]"," ",0,"[(sqrt(2)*a^3*d*sqrt(-1/d)*log((2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) - 1) + tan(f*x + e)^2 - 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e) + 2*(a^3*tan(f*x + e) - a^3)*sqrt(d*tan(f*x + e)))/(d^2*f*tan(f*x + e)), 2*(sqrt(2)*a^3*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e)))*tan(f*x + e) + (a^3*tan(f*x + e) - a^3)*sqrt(d*tan(f*x + e)))/(d^2*f*tan(f*x + e))]","A",0
355,1,228,0,0.519666," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} a^{3} \sqrt{d} \log\left(\frac{\tan\left(f x + e\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) + 1\right)}}{\sqrt{d}} + 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right)^{2} - 2 \, {\left(9 \, a^{3} \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{3 \, d^{3} f \tan\left(f x + e\right)^{2}}, -\frac{2 \, {\left(3 \, \sqrt{2} a^{3} d \sqrt{-\frac{1}{d}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, \tan\left(f x + e\right)}\right) \tan\left(f x + e\right)^{2} + {\left(9 \, a^{3} \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{3 \, d^{3} f \tan\left(f x + e\right)^{2}}\right]"," ",0,"[1/3*(3*sqrt(2)*a^3*sqrt(d)*log((tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) + 1)/sqrt(d) + 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e)^2 - 2*(9*a^3*tan(f*x + e) + a^3)*sqrt(d*tan(f*x + e)))/(d^3*f*tan(f*x + e)^2), -2/3*(3*sqrt(2)*a^3*d*sqrt(-1/d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) + 1)/tan(f*x + e))*tan(f*x + e)^2 + (9*a^3*tan(f*x + e) + a^3)*sqrt(d*tan(f*x + e)))/(d^3*f*tan(f*x + e)^2)]","A",0
356,1,257,0,0.573621," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} a^{3} d \sqrt{-\frac{1}{d}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) - 1\right)} - \tan\left(f x + e\right)^{2} + 4 \, \tan\left(f x + e\right) - 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right)^{3} - 2 \, {\left(10 \, a^{3} \tan\left(f x + e\right)^{2} + 5 \, a^{3} \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{5 \, d^{4} f \tan\left(f x + e\right)^{3}}, -\frac{2 \, {\left(5 \, \sqrt{2} a^{3} \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) \tan\left(f x + e\right)^{3} + {\left(10 \, a^{3} \tan\left(f x + e\right)^{2} + 5 \, a^{3} \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{5 \, d^{4} f \tan\left(f x + e\right)^{3}}\right]"," ",0,"[1/5*(5*sqrt(2)*a^3*d*sqrt(-1/d)*log(-(2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) - 1) - tan(f*x + e)^2 + 4*tan(f*x + e) - 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e)^3 - 2*(10*a^3*tan(f*x + e)^2 + 5*a^3*tan(f*x + e) + a^3)*sqrt(d*tan(f*x + e)))/(d^4*f*tan(f*x + e)^3), -2/5*(5*sqrt(2)*a^3*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e)))*tan(f*x + e)^3 + (10*a^3*tan(f*x + e)^2 + 5*a^3*tan(f*x + e) + a^3)*sqrt(d*tan(f*x + e)))/(d^4*f*tan(f*x + e)^3)]","A",0
357,1,284,0,0.542556," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{2} a^{3} \sqrt{d} \log\left(\frac{\tan\left(f x + e\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) + 1\right)}}{\sqrt{d}} + 4 \, \tan\left(f x + e\right) + 1}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right)^{4} + 2 \, {\left(210 \, a^{3} \tan\left(f x + e\right)^{3} - 70 \, a^{3} \tan\left(f x + e\right)^{2} - 63 \, a^{3} \tan\left(f x + e\right) - 15 \, a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{105 \, d^{5} f \tan\left(f x + e\right)^{4}}, \frac{2 \, {\left(105 \, \sqrt{2} a^{3} d \sqrt{-\frac{1}{d}} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-\frac{1}{d}} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, \tan\left(f x + e\right)}\right) \tan\left(f x + e\right)^{4} + {\left(210 \, a^{3} \tan\left(f x + e\right)^{3} - 70 \, a^{3} \tan\left(f x + e\right)^{2} - 63 \, a^{3} \tan\left(f x + e\right) - 15 \, a^{3}\right)} \sqrt{d \tan\left(f x + e\right)}\right)}}{105 \, d^{5} f \tan\left(f x + e\right)^{4}}\right]"," ",0,"[1/105*(105*sqrt(2)*a^3*sqrt(d)*log((tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) + 1)/sqrt(d) + 4*tan(f*x + e) + 1)/(tan(f*x + e)^2 + 1))*tan(f*x + e)^4 + 2*(210*a^3*tan(f*x + e)^3 - 70*a^3*tan(f*x + e)^2 - 63*a^3*tan(f*x + e) - 15*a^3)*sqrt(d*tan(f*x + e)))/(d^5*f*tan(f*x + e)^4), 2/105*(105*sqrt(2)*a^3*d*sqrt(-1/d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-1/d)*(tan(f*x + e) + 1)/tan(f*x + e))*tan(f*x + e)^4 + (210*a^3*tan(f*x + e)^3 - 70*a^3*tan(f*x + e)^2 - 63*a^3*tan(f*x + e) - 15*a^3)*sqrt(d*tan(f*x + e)))/(d^5*f*tan(f*x + e)^4)]","A",0
358,1,247,0,0.494003," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-d} d^{2} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)} \sqrt{-d} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, \sqrt{-d} d^{2} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) + 8 \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{4 \, a f}, -\frac{\sqrt{2} d^{\frac{5}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) + 2 \, d^{\frac{5}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) - 4 \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{2 \, a f}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(-d)*d^2*log((d*tan(f*x + e)^2 - 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))*sqrt(-d) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 2*sqrt(-d)*d^2*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) + 8*sqrt(d*tan(f*x + e))*d^2)/(a*f), -1/2*(sqrt(2)*d^(5/2)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))/(sqrt(d)*tan(f*x + e))) + 2*d^(5/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) - 4*sqrt(d*tan(f*x + e))*d^2)/(a*f)]","A",0
359,1,211,0,0.506196," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-d} d \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{-d}}{2 \, d \tan\left(f x + e\right)}\right) + \sqrt{-d} d \log\left(\frac{d \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right)}{2 \, a f}, \frac{\sqrt{2} d^{\frac{3}{2}} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{d} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{4 \, a f}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(-d)*d*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(-d)/(d*tan(f*x + e))) + sqrt(-d)*d*log((d*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)))/(a*f), 1/4*(sqrt(2)*d^(3/2)*log((d*tan(f*x + e)^2 - 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(d) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 4*d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)))/(a*f)]","A",0
360,1,211,0,0.471073," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)} \sqrt{-d} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right)}{4 \, a f}, \frac{\sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) - 2 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{2 \, a f}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(-d)*log((d*tan(f*x + e)^2 + 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))*sqrt(-d) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 2*sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)))/(a*f), 1/2*(sqrt(2)*sqrt(d)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))/(sqrt(d)*tan(f*x + e))) - 2*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)))/(a*f)]","A",0
361,1,209,0,0.533993," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) + \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right)}{2 \, a d f}, \frac{\sqrt{2} \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 4 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{4 \, a d f}\right]"," ",0,"[-1/2*(sqrt(2)*sqrt(-d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e))) + sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)))/(a*d*f), 1/4*(sqrt(2)*sqrt(d)*log((d*tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 4*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)))/(a*d*f)]","A",0
362,1,271,0,0.511340," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) - 1\right)} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right) + 2 \, \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) \tan\left(f x + e\right) + 8 \, \sqrt{d \tan\left(f x + e\right)}}{4 \, a d^{2} f \tan\left(f x + e\right)}, -\frac{\sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) \tan\left(f x + e\right) + 2 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) \tan\left(f x + e\right) + 4 \, \sqrt{d \tan\left(f x + e\right)}}{2 \, a d^{2} f \tan\left(f x + e\right)}\right]"," ",0,"[-1/4*(sqrt(2)*sqrt(-d)*log((d*tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) - 1) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1))*tan(f*x + e) + 2*sqrt(-d)*log((d*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1))*tan(f*x + e) + 8*sqrt(d*tan(f*x + e)))/(a*d^2*f*tan(f*x + e)), -1/2*(sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e)))*tan(f*x + e) + 2*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))*tan(f*x + e) + 4*sqrt(d*tan(f*x + e)))/(a*d^2*f*tan(f*x + e))]","A",0
363,1,304,0,0.528874," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} \sqrt{-d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) \tan\left(f x + e\right)^{2} - 3 \, \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) \tan\left(f x + e\right)^{2} + 4 \, \sqrt{d \tan\left(f x + e\right)} {\left(3 \, \tan\left(f x + e\right) - 1\right)}}{6 \, a d^{3} f \tan\left(f x + e\right)^{2}}, \frac{3 \, \sqrt{2} \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) \tan\left(f x + e\right)^{2} + 12 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) \tan\left(f x + e\right)^{2} + 8 \, \sqrt{d \tan\left(f x + e\right)} {\left(3 \, \tan\left(f x + e\right) - 1\right)}}{12 \, a d^{3} f \tan\left(f x + e\right)^{2}}\right]"," ",0,"[1/6*(3*sqrt(2)*sqrt(-d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e)))*tan(f*x + e)^2 - 3*sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1))*tan(f*x + e)^2 + 4*sqrt(d*tan(f*x + e))*(3*tan(f*x + e) - 1))/(a*d^3*f*tan(f*x + e)^2), 1/12*(3*sqrt(2)*sqrt(d)*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1))*tan(f*x + e)^2 + 12*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))*tan(f*x + e)^2 + 8*sqrt(d*tan(f*x + e))*(3*tan(f*x + e) - 1))/(a*d^3*f*tan(f*x + e)^2)]","A",0
364,1,1739,0,0.968641," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) + d^{2}\right)} \sqrt{-d} \log\left(-\frac{6 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - d^{2} + 4 \, {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{-d} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} + d^{10}}{d^{10}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - d^{10}}{d^{10}}\right) - {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(d^{2} \cos\left(f x + e\right)^{2} + d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f\right)}}, \frac{12 \, {\left(2 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) + d^{2}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{\sqrt{d}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} + d^{10}}{d^{10}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - d^{10}}{d^{10}}\right) - {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{10}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{10}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(d^{2} \cos\left(f x + e\right)^{2} + d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[1/8*(3*(2*d^2*cos(f*x + e)*sin(f*x + e) + d^2)*sqrt(-d)*log(-(6*d^2*cos(f*x + e)*sin(f*x + e) - d^2 + 4*(d*cos(f*x + e)^2 - d*cos(f*x + e)*sin(f*x + e))*sqrt(-d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*cos(f*x + e)*sin(f*x + e) + 1)) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) + d^10)/d^10) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) - d^10)/d^10) - (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e)) + (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e)) - 4*(d^2*cos(f*x + e)^2 + d^2*cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f), 1/8*(12*(2*d^2*cos(f*x + e)*sin(f*x + e) + d^2)*sqrt(d)*arctan(sqrt(d*sin(f*x + e)/cos(f*x + e))/sqrt(d)) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) + d^10)/d^10) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e))*(d^10/(a^8*f^4))^(3/4) - d^10)/d^10) - (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e)) + (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^10/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^10/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^10/(a^8*f^4))^(1/4)*cos(f*x + e) + d^5*sin(f*x + e))/cos(f*x + e)) - 4*(d^2*cos(f*x + e)^2 + d^2*cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f)]","B",0
365,1,1754,0,1.062371," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, d \cos\left(f x + e\right) \sin\left(f x + e\right) + d\right)} \sqrt{-d} \log\left(-\frac{6 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - d^{2} - 4 \, {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{-d} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1}\right) - 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{2} d^{4} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} + d^{6} - \sqrt{2} a^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) + d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}}}{d^{6}}\right) - 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{2} d^{4} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} - d^{6} - \sqrt{2} a^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) - d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}}}{d^{6}}\right) - {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) + d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) - d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(d \cos\left(f x + e\right)^{2} + d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f\right)}}, -\frac{4 \, {\left(2 \, d \cos\left(f x + e\right) \sin\left(f x + e\right) + d\right)} \sqrt{d} \arctan\left(\frac{\sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{\sqrt{d}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{2} d^{4} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} + d^{6} - \sqrt{2} a^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) + d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}}}{d^{6}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{2} d^{4} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} - d^{6} - \sqrt{2} a^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) - d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}}}{d^{6}}\right) + {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) + d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{6}}{a^{8} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{d^{6}}{a^{8} f^{4}}} \cos\left(f x + e\right) - d^{9} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(d \cos\left(f x + e\right)^{2} + d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[1/8*((2*d*cos(f*x + e)*sin(f*x + e) + d)*sqrt(-d)*log(-(6*d^2*cos(f*x + e)*sin(f*x + e) - d^2 - 4*(d*cos(f*x + e)^2 - d*cos(f*x + e)*sin(f*x + e))*sqrt(-d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*cos(f*x + e)*sin(f*x + e) + 1)) - 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^2*d^4*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4) + d^6 - sqrt(2)*a^2*f*sqrt((sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) + d^9*sin(f*x + e))/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4))/d^6) - 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^2*d^4*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4) - d^6 - sqrt(2)*a^2*f*sqrt(-(sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) - d^9*sin(f*x + e))/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4))/d^6) - (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*log((sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) + d^9*sin(f*x + e))/cos(f*x + e)) + (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) - d^9*sin(f*x + e))/cos(f*x + e)) + 4*(d*cos(f*x + e)^2 + d*cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f), -1/8*(4*(2*d*cos(f*x + e)*sin(f*x + e) + d)*sqrt(d)*arctan(sqrt(d*sin(f*x + e)/cos(f*x + e))/sqrt(d)) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^2*d^4*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4) + d^6 - sqrt(2)*a^2*f*sqrt((sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) + d^9*sin(f*x + e))/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4))/d^6) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^2*d^4*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4) - d^6 - sqrt(2)*a^2*f*sqrt(-(sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) - d^9*sin(f*x + e))/cos(f*x + e))*(d^6/(a^8*f^4))^(1/4))/d^6) + (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*log((sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) + d^9*sin(f*x + e))/cos(f*x + e)) - (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^6/(a^8*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^6/(a^8*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(d^6/(a^8*f^4))*cos(f*x + e) - d^9*sin(f*x + e))/cos(f*x + e)) - 4*(d*cos(f*x + e)^2 + d*cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f)]","B",0
366,1,1662,0,0.981871," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1\right)} \sqrt{-d} \log\left(-\frac{6 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - d^{2} - 4 \, {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{-d} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1}\right) - 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} + d^{2}}{d^{2}}\right) - 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - d^{2}}{d^{2}}\right) + {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f\right)}}, -\frac{4 \, {\left(2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{\sqrt{d}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} + d^{2}}{d^{2}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} a^{6} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} a^{6} f^{3} \sqrt{\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{3}{4}} - d^{2}}{d^{2}}\right) - {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + {\left(2 \, \sqrt{2} a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} f\right)} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} f^{2} \sqrt{\frac{d^{2}}{a^{8} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{a^{8} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[1/8*((2*cos(f*x + e)*sin(f*x + e) + 1)*sqrt(-d)*log(-(6*d^2*cos(f*x + e)*sin(f*x + e) - d^2 - 4*(d*cos(f*x + e)^2 - d*cos(f*x + e)*sin(f*x + e))*sqrt(-d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*cos(f*x + e)*sin(f*x + e) + 1)) - 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) + d^2)/d^2) - 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) - d^2)/d^2) + (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) - (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) - 4*(cos(f*x + e)^2 + cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f), -1/8*(4*(2*cos(f*x + e)*sin(f*x + e) + 1)*sqrt(d)*arctan(sqrt(d*sin(f*x + e)/cos(f*x + e))/sqrt(d)) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) + d^2)/d^2) + 4*(2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*arctan(-(sqrt(2)*a^6*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) - sqrt(2)*a^6*f^3*sqrt((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(d^2/(a^8*f^4))^(3/4) - d^2)/d^2) - (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) + sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) + (2*sqrt(2)*a^2*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*f)*(d^2/(a^8*f^4))^(1/4)*log((a^4*f^2*sqrt(d^2/(a^8*f^4))*cos(f*x + e) - sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/(a^8*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) + 4*(cos(f*x + e)^2 + cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f)]","B",0
367,1,1707,0,1.116843," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1\right)} \sqrt{-d} \log\left(-\frac{6 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - d^{2} - 4 \, {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{-d} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1}\right) - 4 \, {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} - 1\right) - 4 \, {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} + 1\right) - {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} d f\right)}}, \frac{12 \, {\left(2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{\sqrt{d}}\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} - 1\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} + 1\right) + {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - {\left(2 \, \sqrt{2} a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + \sqrt{2} a^{2} d f\right)} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{2} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{2} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{2} f^{2} \sqrt{\frac{1}{a^{8} d^{2} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(2 \, a^{2} d f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} d f\right)}}\right]"," ",0,"[-1/8*(3*(2*cos(f*x + e)*sin(f*x + e) + 1)*sqrt(-d)*log(-(6*d^2*cos(f*x + e)*sin(f*x + e) - d^2 - 4*(d*cos(f*x + e)^2 - d*cos(f*x + e)*sin(f*x + e))*sqrt(-d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*cos(f*x + e)*sin(f*x + e) + 1)) - 4*(2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*arctan(-sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) + sqrt(2)*a^2*f*sqrt((sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) + a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) - 1) - 4*(2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*arctan(-sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) + sqrt(2)*a^2*f*sqrt(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) - a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) + 1) - (2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*log((sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) + a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) + (2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) - a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e)) - 4*(cos(f*x + e)^2 + cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*d*f*cos(f*x + e)*sin(f*x + e) + a^2*d*f), 1/8*(12*(2*cos(f*x + e)*sin(f*x + e) + 1)*sqrt(d)*arctan(sqrt(d*sin(f*x + e)/cos(f*x + e))/sqrt(d)) + 4*(2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*arctan(-sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) + sqrt(2)*a^2*f*sqrt((sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) + a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) - 1) + 4*(2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*arctan(-sqrt(2)*a^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) + sqrt(2)*a^2*f*sqrt(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) - a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^2*f^4))^(1/4) + 1) + (2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*log((sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) + a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) - (2*sqrt(2)*a^2*d*f*cos(f*x + e)*sin(f*x + e) + sqrt(2)*a^2*d*f)*(1/(a^8*d^2*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^2*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^2*f^4))^(3/4)*cos(f*x + e) - a^4*d^2*f^2*sqrt(1/(a^8*d^2*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e)) + 4*(cos(f*x + e)^2 + cos(f*x + e)*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*a^2*d*f*cos(f*x + e)*sin(f*x + e) + a^2*d*f)]","B",0
368,1,2255,0,1.328420," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{5 \, {\left(\cos\left(f x + e\right)^{2} + 2 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 1\right)} \sqrt{-d} \log\left(-\frac{6 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - d^{2} + 4 \, {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{-d} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1}\right) - 4 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} - 1\right) - 4 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} + 1\right) + {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(9 \, \cos\left(f x + e\right)^{4} - 9 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{2} d^{2} f \cos\left(f x + e\right)^{2} - a^{2} d^{2} f + 2 \, {\left(a^{2} d^{2} f \cos\left(f x + e\right)^{3} - a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}, -\frac{20 \, {\left(\cos\left(f x + e\right)^{2} + 2 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{\sqrt{d}}\right) - 4 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} - 1\right) - 4 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} a^{6} d^{4} f^{3} \sqrt{\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{3}{4}} + 1\right) + {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{2} f + 2 \, {\left(\sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{4} d^{4} f^{2} \sqrt{\frac{1}{a^{8} d^{6} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(9 \, \cos\left(f x + e\right)^{4} - 9 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{2} d^{2} f \cos\left(f x + e\right)^{2} - a^{2} d^{2} f + 2 \, {\left(a^{2} d^{2} f \cos\left(f x + e\right)^{3} - a^{2} d^{2} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/8*(5*(cos(f*x + e)^2 + 2*(cos(f*x + e)^3 - cos(f*x + e))*sin(f*x + e) - 1)*sqrt(-d)*log(-(6*d^2*cos(f*x + e)*sin(f*x + e) - d^2 + 4*(d*cos(f*x + e)^2 - d*cos(f*x + e)*sin(f*x + e))*sqrt(-d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*cos(f*x + e)*sin(f*x + e) + 1)) - 4*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*arctan(-sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) + sqrt(2)*a^6*d^4*f^3*sqrt((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) - 1) - 4*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*arctan(-sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) + sqrt(2)*a^6*d^4*f^3*sqrt((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) + 1) + (sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*log((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) - (sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*log((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) + 4*(9*cos(f*x + e)^4 - 9*cos(f*x + e)^2 + (cos(f*x + e)^3 - 5*cos(f*x + e))*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(a^2*d^2*f*cos(f*x + e)^2 - a^2*d^2*f + 2*(a^2*d^2*f*cos(f*x + e)^3 - a^2*d^2*f*cos(f*x + e))*sin(f*x + e)), -1/8*(20*(cos(f*x + e)^2 + 2*(cos(f*x + e)^3 - cos(f*x + e))*sin(f*x + e) - 1)*sqrt(d)*arctan(sqrt(d*sin(f*x + e)/cos(f*x + e))/sqrt(d)) - 4*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*arctan(-sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) + sqrt(2)*a^6*d^4*f^3*sqrt((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) - 1) - 4*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*arctan(-sqrt(2)*a^6*d^4*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) + sqrt(2)*a^6*d^4*f^3*sqrt((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^6*f^4))^(3/4) + 1) + (sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*log((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) + sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) - (sqrt(2)*a^2*d^2*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^2*f + 2*(sqrt(2)*a^2*d^2*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^2*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*log((a^4*d^4*f^2*sqrt(1/(a^8*d^6*f^4))*cos(f*x + e) - sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^6*f^4))^(1/4)*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) + 4*(9*cos(f*x + e)^4 - 9*cos(f*x + e)^2 + (cos(f*x + e)^3 - 5*cos(f*x + e))*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(a^2*d^2*f*cos(f*x + e)^2 - a^2*d^2*f + 2*(a^2*d^2*f*cos(f*x + e)^3 - a^2*d^2*f*cos(f*x + e))*sin(f*x + e))]","B",0
369,1,2269,0,1.102962," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{21 \, {\left(\cos\left(f x + e\right)^{2} + 2 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 1\right)} \sqrt{-d} \log\left(-\frac{6 \, d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - d^{2} - 4 \, {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{-d} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) + 1}\right) + 12 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} - 1\right) + 12 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} d^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} + 1\right) + 3 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 3 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, {\left(51 \, \cos\left(f x + e\right)^{4} - 47 \, \cos\left(f x + e\right)^{2} + {\left(11 \, \cos\left(f x + e\right)^{3} - 27 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{24 \, {\left(a^{2} d^{3} f \cos\left(f x + e\right)^{2} - a^{2} d^{3} f + 2 \, {\left(a^{2} d^{3} f \cos\left(f x + e\right)^{3} - a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}, \frac{84 \, {\left(\cos\left(f x + e\right)^{2} + 2 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{\sqrt{d}}\right) - 12 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} d^{2} f \sqrt{\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} - 1\right) - 12 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{2} d^{2} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} d^{2} f \sqrt{-\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} + 1\right) - 3 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 3 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{2} - \sqrt{2} a^{2} d^{3} f + 2 \, {\left(\sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)^{3} - \sqrt{2} a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} a^{6} d^{8} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{1}{a^{8} d^{10} f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - a^{4} d^{6} f^{2} \sqrt{\frac{1}{a^{8} d^{10} f^{4}}} \cos\left(f x + e\right) - d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(51 \, \cos\left(f x + e\right)^{4} - 47 \, \cos\left(f x + e\right)^{2} + {\left(11 \, \cos\left(f x + e\right)^{3} - 27 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{24 \, {\left(a^{2} d^{3} f \cos\left(f x + e\right)^{2} - a^{2} d^{3} f + 2 \, {\left(a^{2} d^{3} f \cos\left(f x + e\right)^{3} - a^{2} d^{3} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/24*(21*(cos(f*x + e)^2 + 2*(cos(f*x + e)^3 - cos(f*x + e))*sin(f*x + e) - 1)*sqrt(-d)*log(-(6*d^2*cos(f*x + e)*sin(f*x + e) - d^2 - 4*(d*cos(f*x + e)^2 - d*cos(f*x + e)*sin(f*x + e))*sqrt(-d)*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(2*cos(f*x + e)*sin(f*x + e) + 1)) + 12*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*arctan(-sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) + sqrt(2)*a^2*d^2*f*sqrt((sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) - 1) + 12*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*arctan(-sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) + sqrt(2)*a^2*d^2*f*sqrt(-(sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) + 1) + 3*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*log((sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) - 3*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e)) - 4*(51*cos(f*x + e)^4 - 47*cos(f*x + e)^2 + (11*cos(f*x + e)^3 - 27*cos(f*x + e))*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(a^2*d^3*f*cos(f*x + e)^2 - a^2*d^3*f + 2*(a^2*d^3*f*cos(f*x + e)^3 - a^2*d^3*f*cos(f*x + e))*sin(f*x + e)), 1/24*(84*(cos(f*x + e)^2 + 2*(cos(f*x + e)^3 - cos(f*x + e))*sin(f*x + e) - 1)*sqrt(d)*arctan(sqrt(d*sin(f*x + e)/cos(f*x + e))/sqrt(d)) - 12*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*arctan(-sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) + sqrt(2)*a^2*d^2*f*sqrt((sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) - 1) - 12*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*arctan(-sqrt(2)*a^2*d^2*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) + sqrt(2)*a^2*d^2*f*sqrt(-(sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e))*(1/(a^8*d^10*f^4))^(1/4) + 1) - 3*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*log((sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) + a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)) + 3*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^2 - sqrt(2)*a^2*d^3*f + 2*(sqrt(2)*a^2*d^3*f*cos(f*x + e)^3 - sqrt(2)*a^2*d^3*f*cos(f*x + e))*sin(f*x + e))*(1/(a^8*d^10*f^4))^(1/4)*log(-(sqrt(2)*a^6*d^8*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(1/(a^8*d^10*f^4))^(3/4)*cos(f*x + e) - a^4*d^6*f^2*sqrt(1/(a^8*d^10*f^4))*cos(f*x + e) - d*sin(f*x + e))/cos(f*x + e)) + 4*(51*cos(f*x + e)^4 - 47*cos(f*x + e)^2 + (11*cos(f*x + e)^3 - 27*cos(f*x + e))*sin(f*x + e))*sqrt(d*sin(f*x + e)/cos(f*x + e)))/(a^2*d^3*f*cos(f*x + e)^2 - a^2*d^3*f + 2*(a^2*d^3*f*cos(f*x + e)^3 - a^2*d^3*f*cos(f*x + e))*sin(f*x + e))]","B",0
370,1,472,0,0.688798," ","integrate((d*tan(f*x+e))^(9/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(\sqrt{2} d^{4} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d^{4} \tan\left(f x + e\right) + \sqrt{2} d^{4}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{-d}}{2 \, d \tan\left(f x + e\right)}\right) - 31 \, {\left(d^{4} \tan\left(f x + e\right)^{2} + 2 \, d^{4} \tan\left(f x + e\right) + d^{4}\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) - 2 \, {\left(16 \, d^{4} \tan\left(f x + e\right)^{2} + 45 \, d^{4} \tan\left(f x + e\right) + 27 \, d^{4}\right)} \sqrt{d \tan\left(f x + e\right)}}{16 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}, -\frac{31 \, {\left(d^{4} \tan\left(f x + e\right)^{2} + 2 \, d^{4} \tan\left(f x + e\right) + d^{4}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) - {\left(\sqrt{2} d^{4} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d^{4} \tan\left(f x + e\right) + \sqrt{2} d^{4}\right)} \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{d} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(16 \, d^{4} \tan\left(f x + e\right)^{2} + 45 \, d^{4} \tan\left(f x + e\right) + 27 \, d^{4}\right)} \sqrt{d \tan\left(f x + e\right)}}{8 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[-1/16*(4*(sqrt(2)*d^4*tan(f*x + e)^2 + 2*sqrt(2)*d^4*tan(f*x + e) + sqrt(2)*d^4)*sqrt(-d)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(-d)/(d*tan(f*x + e))) - 31*(d^4*tan(f*x + e)^2 + 2*d^4*tan(f*x + e) + d^4)*sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) - 2*(16*d^4*tan(f*x + e)^2 + 45*d^4*tan(f*x + e) + 27*d^4)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f), -1/8*(31*(d^4*tan(f*x + e)^2 + 2*d^4*tan(f*x + e) + d^4)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) - (sqrt(2)*d^4*tan(f*x + e)^2 + 2*sqrt(2)*d^4*tan(f*x + e) + sqrt(2)*d^4)*sqrt(d)*log((d*tan(f*x + e)^2 + 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(d) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) - (16*d^4*tan(f*x + e)^2 + 45*d^4*tan(f*x + e) + 27*d^4)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f)]","A",0
371,1,447,0,0.552335," ","integrate((d*tan(f*x+e))^(7/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(\sqrt{2} d^{3} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d^{3} \tan\left(f x + e\right) + \sqrt{2} d^{3}\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)} \sqrt{-d} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 11 \, {\left(d^{3} \tan\left(f x + e\right)^{2} + 2 \, d^{3} \tan\left(f x + e\right) + d^{3}\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) - 2 \, {\left(9 \, d^{3} \tan\left(f x + e\right) + 7 \, d^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{16 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}, \frac{11 \, {\left(d^{3} \tan\left(f x + e\right)^{2} + 2 \, d^{3} \tan\left(f x + e\right) + d^{3}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) - 2 \, {\left(\sqrt{2} d^{3} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d^{3} \tan\left(f x + e\right) + \sqrt{2} d^{3}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) - {\left(9 \, d^{3} \tan\left(f x + e\right) + 7 \, d^{3}\right)} \sqrt{d \tan\left(f x + e\right)}}{8 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[1/16*(2*(sqrt(2)*d^3*tan(f*x + e)^2 + 2*sqrt(2)*d^3*tan(f*x + e) + sqrt(2)*d^3)*sqrt(-d)*log((d*tan(f*x + e)^2 - 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))*sqrt(-d) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 11*(d^3*tan(f*x + e)^2 + 2*d^3*tan(f*x + e) + d^3)*sqrt(-d)*log((d*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) - 2*(9*d^3*tan(f*x + e) + 7*d^3)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f), 1/8*(11*(d^3*tan(f*x + e)^2 + 2*d^3*tan(f*x + e) + d^3)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) - 2*(sqrt(2)*d^3*tan(f*x + e)^2 + 2*sqrt(2)*d^3*tan(f*x + e) + sqrt(2)*d^3)*sqrt(d)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))/(sqrt(d)*tan(f*x + e))) - (9*d^3*tan(f*x + e) + 7*d^3)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f)]","A",0
372,1,442,0,0.592066," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(\sqrt{2} d^{2} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d^{2} \tan\left(f x + e\right) + \sqrt{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{-d}}{2 \, d \tan\left(f x + e\right)}\right) + {\left(d^{2} \tan\left(f x + e\right)^{2} + 2 \, d^{2} \tan\left(f x + e\right) + d^{2}\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) + 2 \, {\left(5 \, d^{2} \tan\left(f x + e\right) + 3 \, d^{2}\right)} \sqrt{d \tan\left(f x + e\right)}}{16 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}, \frac{{\left(d^{2} \tan\left(f x + e\right)^{2} + 2 \, d^{2} \tan\left(f x + e\right) + d^{2}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) + {\left(\sqrt{2} d^{2} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d^{2} \tan\left(f x + e\right) + \sqrt{2} d^{2}\right)} \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{d} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(5 \, d^{2} \tan\left(f x + e\right) + 3 \, d^{2}\right)} \sqrt{d \tan\left(f x + e\right)}}{8 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[1/16*(4*(sqrt(2)*d^2*tan(f*x + e)^2 + 2*sqrt(2)*d^2*tan(f*x + e) + sqrt(2)*d^2)*sqrt(-d)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(-d)/(d*tan(f*x + e))) + (d^2*tan(f*x + e)^2 + 2*d^2*tan(f*x + e) + d^2)*sqrt(-d)*log((d*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) + 2*(5*d^2*tan(f*x + e) + 3*d^2)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f), 1/8*((d^2*tan(f*x + e)^2 + 2*d^2*tan(f*x + e) + d^2)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) + (sqrt(2)*d^2*tan(f*x + e)^2 + 2*sqrt(2)*d^2*tan(f*x + e) + sqrt(2)*d^2)*sqrt(d)*log((d*tan(f*x + e)^2 - 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(d) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + (5*d^2*tan(f*x + e) + 3*d^2)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f)]","A",0
373,1,412,0,0.662380," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(\sqrt{2} d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d \tan\left(f x + e\right) + \sqrt{2} d\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)} \sqrt{-d} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 5 \, {\left(d \tan\left(f x + e\right)^{2} + 2 \, d \tan\left(f x + e\right) + d\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) - 2 \, {\left(d \tan\left(f x + e\right) - d\right)} \sqrt{d \tan\left(f x + e\right)}}{16 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}, -\frac{5 \, {\left(d \tan\left(f x + e\right)^{2} + 2 \, d \tan\left(f x + e\right) + d\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) - 2 \, {\left(\sqrt{2} d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} d \tan\left(f x + e\right) + \sqrt{2} d\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) - \sqrt{2}\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) + {\left(d \tan\left(f x + e\right) - d\right)} \sqrt{d \tan\left(f x + e\right)}}{8 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[1/16*(2*(sqrt(2)*d*tan(f*x + e)^2 + 2*sqrt(2)*d*tan(f*x + e) + sqrt(2)*d)*sqrt(-d)*log((d*tan(f*x + e)^2 + 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))*sqrt(-d) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 5*(d*tan(f*x + e)^2 + 2*d*tan(f*x + e) + d)*sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) - 2*(d*tan(f*x + e) - d)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f), -1/8*(5*(d*tan(f*x + e)^2 + 2*d*tan(f*x + e) + d)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) - 2*(sqrt(2)*d*tan(f*x + e)^2 + 2*sqrt(2)*d*tan(f*x + e) + sqrt(2)*d)*sqrt(d)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) - sqrt(2))/(sqrt(d)*tan(f*x + e))) + (d*tan(f*x + e) - d)*sqrt(d*tan(f*x + e)))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f)]","A",0
374,1,392,0,0.673624," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(\sqrt{2} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{-d}}{2 \, d \tan\left(f x + e\right)}\right) - {\left(\tan\left(f x + e\right)^{2} + 2 \, \tan\left(f x + e\right) + 1\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(3 \, \tan\left(f x + e\right) + 5\right)}}{16 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}, \frac{{\left(\tan\left(f x + e\right)^{2} + 2 \, \tan\left(f x + e\right) + 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) + {\left(\sqrt{2} \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(\sqrt{2} \tan\left(f x + e\right) + \sqrt{2}\right)} \sqrt{d} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) - \sqrt{d \tan\left(f x + e\right)} {\left(3 \, \tan\left(f x + e\right) + 5\right)}}{8 \, {\left(a^{3} f \tan\left(f x + e\right)^{2} + 2 \, a^{3} f \tan\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[-1/16*(4*(sqrt(2)*tan(f*x + e)^2 + 2*sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(-d)*arctan(1/2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(-d)/(d*tan(f*x + e))) - (tan(f*x + e)^2 + 2*tan(f*x + e) + 1)*sqrt(-d)*log((d*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) + 2*sqrt(d*tan(f*x + e))*(3*tan(f*x + e) + 5))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f), 1/8*((tan(f*x + e)^2 + 2*tan(f*x + e) + 1)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) + (sqrt(2)*tan(f*x + e)^2 + 2*sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(d)*log((d*tan(f*x + e)^2 + 2*sqrt(d*tan(f*x + e))*(sqrt(2)*tan(f*x + e) + sqrt(2))*sqrt(d) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) - sqrt(d*tan(f*x + e))*(3*tan(f*x + e) + 5))/(a^3*f*tan(f*x + e)^2 + 2*a^3*f*tan(f*x + e) + a^3*f)]","A",0
375,1,379,0,0.531525," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{2} {\left(\tan\left(f x + e\right)^{2} + 2 \, \tan\left(f x + e\right) + 1\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) - 1\right)} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 11 \, {\left(\tan\left(f x + e\right)^{2} + 2 \, \tan\left(f x + e\right) + 1\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(7 \, \tan\left(f x + e\right) + 9\right)}}{16 \, {\left(a^{3} d f \tan\left(f x + e\right)^{2} + 2 \, a^{3} d f \tan\left(f x + e\right) + a^{3} d f\right)}}, -\frac{2 \, \sqrt{2} {\left(\tan\left(f x + e\right)^{2} + 2 \, \tan\left(f x + e\right) + 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) - 11 \, {\left(\tan\left(f x + e\right)^{2} + 2 \, \tan\left(f x + e\right) + 1\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) - \sqrt{d \tan\left(f x + e\right)} {\left(7 \, \tan\left(f x + e\right) + 9\right)}}{8 \, {\left(a^{3} d f \tan\left(f x + e\right)^{2} + 2 \, a^{3} d f \tan\left(f x + e\right) + a^{3} d f\right)}}\right]"," ",0,"[-1/16*(2*sqrt(2)*(tan(f*x + e)^2 + 2*tan(f*x + e) + 1)*sqrt(-d)*log((d*tan(f*x + e)^2 + 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) - 1) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 11*(tan(f*x + e)^2 + 2*tan(f*x + e) + 1)*sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) - 2*sqrt(d*tan(f*x + e))*(7*tan(f*x + e) + 9))/(a^3*d*f*tan(f*x + e)^2 + 2*a^3*d*f*tan(f*x + e) + a^3*d*f), -1/8*(2*sqrt(2)*(tan(f*x + e)^2 + 2*tan(f*x + e) + 1)*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e))) - 11*(tan(f*x + e)^2 + 2*tan(f*x + e) + 1)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) - sqrt(d*tan(f*x + e))*(7*tan(f*x + e) + 9))/(a^3*d*f*tan(f*x + e)^2 + 2*a^3*d*f*tan(f*x + e) + a^3*d*f)]","A",0
376,1,457,0,0.576837," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(\tan\left(f x + e\right)^{3} + 2 \, \tan\left(f x + e\right)^{2} + \tan\left(f x + e\right)\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) + 1\right)}}{2 \, d \tan\left(f x + e\right)}\right) - 31 \, {\left(\tan\left(f x + e\right)^{3} + 2 \, \tan\left(f x + e\right)^{2} + \tan\left(f x + e\right)\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) + 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} {\left(27 \, \tan\left(f x + e\right)^{2} + 45 \, \tan\left(f x + e\right) + 16\right)}}{16 \, {\left(a^{3} d^{2} f \tan\left(f x + e\right)^{3} + 2 \, a^{3} d^{2} f \tan\left(f x + e\right)^{2} + a^{3} d^{2} f \tan\left(f x + e\right)\right)}}, \frac{\sqrt{2} {\left(\tan\left(f x + e\right)^{3} + 2 \, \tan\left(f x + e\right)^{2} + \tan\left(f x + e\right)\right)} \sqrt{d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} {\left(\tan\left(f x + e\right) + 1\right)} + 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) - 31 \, {\left(\tan\left(f x + e\right)^{3} + 2 \, \tan\left(f x + e\right)^{2} + \tan\left(f x + e\right)\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) - \sqrt{d \tan\left(f x + e\right)} {\left(27 \, \tan\left(f x + e\right)^{2} + 45 \, \tan\left(f x + e\right) + 16\right)}}{8 \, {\left(a^{3} d^{2} f \tan\left(f x + e\right)^{3} + 2 \, a^{3} d^{2} f \tan\left(f x + e\right)^{2} + a^{3} d^{2} f \tan\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(4*sqrt(2)*(tan(f*x + e)^3 + 2*tan(f*x + e)^2 + tan(f*x + e))*sqrt(-d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) + 1)/(d*tan(f*x + e))) - 31*(tan(f*x + e)^3 + 2*tan(f*x + e)^2 + tan(f*x + e))*sqrt(-d)*log((d*tan(f*x + e) + 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) - 2*sqrt(d*tan(f*x + e))*(27*tan(f*x + e)^2 + 45*tan(f*x + e) + 16))/(a^3*d^2*f*tan(f*x + e)^3 + 2*a^3*d^2*f*tan(f*x + e)^2 + a^3*d^2*f*tan(f*x + e)), 1/8*(sqrt(2)*(tan(f*x + e)^3 + 2*tan(f*x + e)^2 + tan(f*x + e))*sqrt(d)*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d)*(tan(f*x + e) + 1) + 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) - 31*(tan(f*x + e)^3 + 2*tan(f*x + e)^2 + tan(f*x + e))*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) - sqrt(d*tan(f*x + e))*(27*tan(f*x + e)^2 + 45*tan(f*x + e) + 16))/(a^3*d^2*f*tan(f*x + e)^3 + 2*a^3*d^2*f*tan(f*x + e)^2 + a^3*d^2*f*tan(f*x + e))]","A",0
377,1,486,0,0.773357," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{2} {\left(\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{3} + \tan\left(f x + e\right)^{2}\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} {\left(\tan\left(f x + e\right) - 1\right)} - 4 \, d \tan\left(f x + e\right) + d}{\tan\left(f x + e\right)^{2} + 1}\right) + 177 \, {\left(\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{3} + \tan\left(f x + e\right)^{2}\right)} \sqrt{-d} \log\left(\frac{d \tan\left(f x + e\right) - 2 \, \sqrt{d \tan\left(f x + e\right)} \sqrt{-d} - d}{\tan\left(f x + e\right) + 1}\right) - 2 \, {\left(189 \, \tan\left(f x + e\right)^{3} + 323 \, \tan\left(f x + e\right)^{2} + 112 \, \tan\left(f x + e\right) - 16\right)} \sqrt{d \tan\left(f x + e\right)}}{48 \, {\left(a^{3} d^{3} f \tan\left(f x + e\right)^{4} + 2 \, a^{3} d^{3} f \tan\left(f x + e\right)^{3} + a^{3} d^{3} f \tan\left(f x + e\right)^{2}\right)}}, \frac{6 \, \sqrt{2} {\left(\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{3} + \tan\left(f x + e\right)^{2}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{2} \sqrt{d \tan\left(f x + e\right)} {\left(\tan\left(f x + e\right) - 1\right)}}{2 \, \sqrt{d} \tan\left(f x + e\right)}\right) + 177 \, {\left(\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{3} + \tan\left(f x + e\right)^{2}\right)} \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right) + {\left(189 \, \tan\left(f x + e\right)^{3} + 323 \, \tan\left(f x + e\right)^{2} + 112 \, \tan\left(f x + e\right) - 16\right)} \sqrt{d \tan\left(f x + e\right)}}{24 \, {\left(a^{3} d^{3} f \tan\left(f x + e\right)^{4} + 2 \, a^{3} d^{3} f \tan\left(f x + e\right)^{3} + a^{3} d^{3} f \tan\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/48*(6*sqrt(2)*(tan(f*x + e)^4 + 2*tan(f*x + e)^3 + tan(f*x + e)^2)*sqrt(-d)*log((d*tan(f*x + e)^2 - 2*sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(-d)*(tan(f*x + e) - 1) - 4*d*tan(f*x + e) + d)/(tan(f*x + e)^2 + 1)) + 177*(tan(f*x + e)^4 + 2*tan(f*x + e)^3 + tan(f*x + e)^2)*sqrt(-d)*log((d*tan(f*x + e) - 2*sqrt(d*tan(f*x + e))*sqrt(-d) - d)/(tan(f*x + e) + 1)) - 2*(189*tan(f*x + e)^3 + 323*tan(f*x + e)^2 + 112*tan(f*x + e) - 16)*sqrt(d*tan(f*x + e)))/(a^3*d^3*f*tan(f*x + e)^4 + 2*a^3*d^3*f*tan(f*x + e)^3 + a^3*d^3*f*tan(f*x + e)^2), 1/24*(6*sqrt(2)*(tan(f*x + e)^4 + 2*tan(f*x + e)^3 + tan(f*x + e)^2)*sqrt(d)*arctan(1/2*sqrt(2)*sqrt(d*tan(f*x + e))*(tan(f*x + e) - 1)/(sqrt(d)*tan(f*x + e))) + 177*(tan(f*x + e)^4 + 2*tan(f*x + e)^3 + tan(f*x + e)^2)*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d)) + (189*tan(f*x + e)^3 + 323*tan(f*x + e)^2 + 112*tan(f*x + e) - 16)*sqrt(d*tan(f*x + e)))/(a^3*d^3*f*tan(f*x + e)^4 + 2*a^3*d^3*f*tan(f*x + e)^3 + a^3*d^3*f*tan(f*x + e)^2)]","A",0
378,1,1042,0,0.531447," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^5,x, algorithm=""fricas"")","\frac{1260 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{4} + 1260 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{4} - 315 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{4} + 2 \, f \cos\left(f x + e\right)^{4}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 315 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{4} + 2 \, f \cos\left(f x + e\right)^{4}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 16 \, {\left(445 \, \cos\left(f x + e\right)^{4} - 139 \, \cos\left(f x + e\right)^{2} - {\left(18 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) + 35\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2520 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/2520*(1260*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^4 + 1260*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^4 - 315*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^4 + 2*f*cos(f*x + e)^4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 315*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^4 + 2*f*cos(f*x + e)^4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 16*(445*cos(f*x + e)^4 - 139*cos(f*x + e)^2 - (18*cos(f*x + e)^3 - 5*cos(f*x + e))*sin(f*x + e) + 35)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^4)","B",0
379,1,1019,0,0.599756," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^3,x, algorithm=""fricas"")","-\frac{60 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{2} + 60 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{2} - 15 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{2} + 2 \, f \cos\left(f x + e\right)^{2}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 15 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{2} + 2 \, f \cos\left(f x + e\right)^{2}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 16 \, {\left(20 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) \sin\left(f x + e\right) - 3\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{120 \, f \cos\left(f x + e\right)^{2}}"," ",0,"-1/120*(60*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^2 + 60*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^2 - 15*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^2 + 2*f*cos(f*x + e)^2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 15*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^2 + 2*f*cos(f*x + e)^2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 16*(20*cos(f*x + e)^2 - cos(f*x + e)*sin(f*x + e) - 3)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^2)","B",0
380,1,936,0,0.507631," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e),x, algorithm=""fricas"")","\frac{4 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) + 4 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 16 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, f}"," ",0,"1/8*(4*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2)) + 4*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2)) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 16*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/f","B",0
381,1,968,0,0.582164," ","integrate(cot(f*x+e)*(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{4 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) + 4 \cdot 2^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 8 \, \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) - 8 \, \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right)}{8 \, f}"," ",0,"-1/8*(4*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2)) + 4*2^(3/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2)) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 8*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) - 8*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1))/f","B",0
382,1,1143,0,0.541858," ","integrate(cot(f*x+e)^3*(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 9 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 9 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(2 \, \cos\left(f x + e\right)^{2} + \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \frac{4 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} - \frac{4 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{8 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"-1/8*(2^(1/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 2^(1/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 9*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 9*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(2*cos(f*x + e)^2 + cos(f*x + e)*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 4*2^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 - 4*2^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^2 - f)","B",0
383,1,1262,0,0.499301," ","integrate(cot(f*x+e)^5*(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{48 \cdot 2^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 48 \cdot 2^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 417 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 417 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(154 \, \cos\left(f x + e\right)^{4} - 106 \, \cos\left(f x + e\right)^{2} + {\left(41 \, \cos\left(f x + e\right)^{3} - 33 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \frac{192 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} - \frac{192 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{384 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"1/384*(48*2^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 48*2^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 417*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 417*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(154*cos(f*x + e)^4 - 106*cos(f*x + e)^2 + (41*cos(f*x + e)^3 - 33*cos(f*x + e))*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 192*2^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 - 192*2^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + 2*f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/2*2^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
384,1,898,0,0.620018," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^4,x, algorithm=""fricas"")","-\frac{140 \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{3} + 140 \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{3} - 35 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{3} - 2 \, f \cos\left(f x + e\right)^{3}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 35 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{3} - 2 \, f \cos\left(f x + e\right)^{3}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 16 \, {\left(10 \, \cos\left(f x + e\right)^{3} + {\left(18 \, \cos\left(f x + e\right)^{2} - 5\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{280 \, f \cos\left(f x + e\right)^{3}}"," ",0,"-1/280*(140*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^3 + 140*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt(-(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^3 - 35*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^3 - 2*f*cos(f*x + e)^3)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 35*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^3 - 2*f*cos(f*x + e)^3)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(-1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e)) + 16*(10*cos(f*x + e)^3 + (18*cos(f*x + e)^2 - 5)*sin(f*x + e) - cos(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^3)","B",0
385,1,861,0,0.929074," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^2,x, algorithm=""fricas"")","\frac{12 \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right) + 12 \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right) - 3 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, f \cos\left(f x + e\right)\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 3 \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, f \cos\left(f x + e\right)\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 16 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right)\right)}}{24 \, f \cos\left(f x + e\right)}"," ",0,"1/24*(12*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e) + 12*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt(-(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e) - 3*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) - 2*f*cos(f*x + e))*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 3*2^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) - 2*f*cos(f*x + e))*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(-1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e)) + 16*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(cos(f*x + e) + sin(f*x + e)))/(f*cos(f*x + e))","B",0
386,1,767,0,0.486090," ","integrate((1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(\sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} - 2\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - \frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(\sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} - 2\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)"," ",0,"1/8*2^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(sqrt(2)*f^2*sqrt(f^(-4)) - 2)*(f^(-4))^(1/4)*log(1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 1/8*2^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(sqrt(2)*f^2*sqrt(f^(-4)) - 2)*(f^(-4))^(1/4)*log(-1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e)) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - f^2*sqrt(f^(-4)) - sqrt(2)) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt(-(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) + f^2*sqrt(f^(-4)) + sqrt(2))","B",0
387,1,1000,0,0.557620," ","integrate(cot(f*x+e)^2*(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) + 8 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 4 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 4 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) + \frac{4 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} + \frac{4 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{8 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"1/8*(2^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 2^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(-1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e)) + 8*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 4*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 4*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) + 4*2^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 + 4*2^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt(-(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^2 - f)","B",0
388,1,1132,0,0.595733," ","integrate(cot(f*x+e)^4*(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{6 \cdot 2^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 6 \cdot 2^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{2 \, \cos\left(f x + e\right)}\right) - 21 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 21 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(2 \, \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} - {\left(35 \, \cos\left(f x + e\right)^{3} - 27 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \frac{24 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) + 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} + \frac{24 \cdot 2^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{-\frac{2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} \cos\left(f x + e\right) - 2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{5} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{5}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{48 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"-1/48*(6*2^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 6*2^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(-1/2*(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e)) - 21*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 21*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(2*cos(f*x + e)^4 - 2*cos(f*x + e)^2 - (35*cos(f*x + e)^3 - 27*cos(f*x + e))*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 24*2^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) + 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 + 24*2^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/2*2^(3/4)*sqrt(1/2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt(-(2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4)*cos(f*x + e) - 2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*cos(f*x + e) - 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) - 1/2*2^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^5*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(5/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
389,1,917,0,0.566101," ","integrate(tan(f*x+e)^5*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{924 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{5} + 924 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{5} + 231 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{5} - 2 \, f \cos\left(f x + e\right)^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 231 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{5} - 2 \, f \cos\left(f x + e\right)^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) + 16 \, {\left(400 \, \cos\left(f x + e\right)^{5} - 110 \, \cos\left(f x + e\right)^{3} + {\left(125 \, \cos\left(f x + e\right)^{4} - 74 \, \cos\left(f x + e\right)^{2} + 21\right)} \sin\left(f x + e\right) + 28 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{1848 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/1848*(924*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^5 + 924*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^5 + 231*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^5 - 2*f*cos(f*x + e)^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 231*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^5 - 2*f*cos(f*x + e)^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 16*(400*cos(f*x + e)^5 - 110*cos(f*x + e)^3 + (125*cos(f*x + e)^4 - 74*cos(f*x + e)^2 + 21)*sin(f*x + e) + 28*cos(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^5)","B",0
390,1,897,0,0.648156," ","integrate(tan(f*x+e)^3*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{420 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{3} + 420 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{3} + 105 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{3} - 2 \, f \cos\left(f x + e\right)^{3}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 105 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{3} - 2 \, f \cos\left(f x + e\right)^{3}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) + 16 \, {\left(170 \, \cos\left(f x + e\right)^{3} + {\left(47 \, \cos\left(f x + e\right)^{2} - 15\right)} \sin\left(f x + e\right) - 24 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{840 \, f \cos\left(f x + e\right)^{3}}"," ",0,"-1/840*(420*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^3 + 420*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^3 + 105*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^3 - 2*f*cos(f*x + e)^3)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 105*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^3 - 2*f*cos(f*x + e)^3)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 16*(170*cos(f*x + e)^3 + (47*cos(f*x + e)^2 - 15)*sin(f*x + e) - 24*cos(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^3)","B",0
391,1,862,0,0.557678," ","integrate(tan(f*x+e)*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{12 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right) + 12 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right) + 3 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, f \cos\left(f x + e\right)\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 3 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, f \cos\left(f x + e\right)\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) + 16 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} {\left(4 \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right)}}{24 \, f \cos\left(f x + e\right)}"," ",0,"1/24*(12*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e) + 12*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e) + 3*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) - 2*f*cos(f*x + e))*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 3*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) - 2*f*cos(f*x + e))*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 16*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(4*cos(f*x + e) + sin(f*x + e)))/(f*cos(f*x + e))","B",0
392,1,834,0,0.579227," ","integrate(cot(f*x+e)*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{4 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) + 4 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) + 8 \, \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) - 8 \, \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right)}{8 \, f}"," ",0,"-1/8*(4*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2)) + 4*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2)) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) - 2*f)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) - 2*f)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 8*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) - 8*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1))/f","B",0
393,1,1012,0,0.496962," ","integrate(cot(f*x+e)^3*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 5 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 5 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(2 \, \cos\left(f x + e\right)^{2} + 5 \, \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \frac{4 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} - \frac{4 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{8 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"-1/8*(8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 5*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 5*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(2*cos(f*x + e)^2 + 5*cos(f*x + e)*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 4*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 - 4*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^2 - f)","B",0
394,1,1130,0,0.581407," ","integrate(cot(f*x+e)^5*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{16 \cdot 8^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 16 \cdot 8^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} - \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 83 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 83 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(46 \, \cos\left(f x + e\right)^{4} - 30 \, \cos\left(f x + e\right)^{2} + {\left(107 \, \cos\left(f x + e\right)^{3} - 83 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \frac{64 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} - \frac{64 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(-\frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + \frac{1}{8} \cdot 8^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f^{3} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{128 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"1/128*(16*8^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 16*8^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 - sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 83*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 83*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(46*cos(f*x + e)^4 - 30*cos(f*x + e)^2 + (107*cos(f*x + e)^3 - 83*cos(f*x + e))*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 64*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 - 64*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(-1/8*8^(3/4)*sqrt(2)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + 1/8*8^(3/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f^3*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*sqrt(2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
395,1,1048,0,0.884665," ","integrate(tan(f*x+e)^4*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{252 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{4} + 252 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{4} + 63 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{4} + 2 \, f \cos\left(f x + e\right)^{4}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 63 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{4} + 2 \, f \cos\left(f x + e\right)^{4}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 16 \, {\left(71 \, \cos\left(f x + e\right)^{4} - 26 \, \cos\left(f x + e\right)^{2} - 2 \, {\left(18 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) + 7\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{504 \, f \cos\left(f x + e\right)^{4}}"," ",0,"-1/504*(252*8^(1/4)*sqrt(2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^4 + 252*8^(1/4)*sqrt(2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^4 + 63*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^4 + 2*f*cos(f*x + e)^4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 63*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^4 + 2*f*cos(f*x + e)^4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 16*(71*cos(f*x + e)^4 - 26*cos(f*x + e)^2 - 2*(18*cos(f*x + e)^3 - 5*cos(f*x + e))*sin(f*x + e) + 7)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^4)","B",0
396,1,1025,0,0.954556," ","integrate(tan(f*x+e)^2*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{20 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) \cos\left(f x + e\right)^{2} + 20 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) \cos\left(f x + e\right)^{2} + 5 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{2} + 2 \, f \cos\left(f x + e\right)^{2}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 5 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{2} + 2 \, f \cos\left(f x + e\right)^{2}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 16 \, {\left(5 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) \sin\left(f x + e\right) - 1\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{40 \, f \cos\left(f x + e\right)^{2}}"," ",0,"1/40*(20*8^(1/4)*sqrt(2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))*cos(f*x + e)^2 + 20*8^(1/4)*sqrt(2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))*cos(f*x + e)^2 + 5*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^2 + 2*f*cos(f*x + e)^2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 5*8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e)^2 + 2*f*cos(f*x + e)^2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 16*(5*cos(f*x + e)^2 - 2*cos(f*x + e)*sin(f*x + e) - 1)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^2)","B",0
397,1,942,0,0.503470," ","integrate((1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{4 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right) + 4 \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 16 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{8 \, f}"," ",0,"-1/8*(4*8^(1/4)*sqrt(2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2)) + 4*8^(1/4)*sqrt(2)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2)) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 16*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/f","B",0
398,1,1137,0,0.723678," ","integrate(cot(f*x+e)^2*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{8^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 8^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(2 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - 2 \, f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) + 8 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 12 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 12 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) + \frac{4 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} + \frac{4 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{8 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"1/8*(8^(1/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 8^(1/4)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(2*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - 2*f)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) + 8*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 12*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 12*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) + 4*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 + 4*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^2 - f)","B",0
399,1,1269,0,0.591702," ","integrate(cot(f*x+e)^4*(1+tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{6 \cdot 8^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 6 \cdot 8^{\frac{1}{4}} {\left(2 \, f \cos\left(f x + e\right)^{4} - 4 \, f \cos\left(f x + e\right)^{2} + \sqrt{2} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + 2 \, f\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)}}{\cos\left(f x + e\right)}\right) - 75 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 75 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(14 \, \cos\left(f x + e\right)^{4} - 14 \, \cos\left(f x + e\right)^{2} - {\left(29 \, \cos\left(f x + e\right)^{3} - 21 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \frac{24 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - \sqrt{2}\right)}{f^{4}} + \frac{24 \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(\frac{1}{16} \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 8^{\frac{1}{4}} {\left(\sqrt{2} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + 2 \, \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - \frac{1}{8} \cdot 8^{\frac{3}{4}} {\left(2 \, f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{2} f^{3}\right)} \sqrt{-2 \, \sqrt{2} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + \sqrt{2}\right)}{f^{4}}}{48 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"-1/48*(6*8^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 6*8^(1/4)*(2*f*cos(f*x + e)^4 - 4*f*cos(f*x + e)^2 + sqrt(2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + 2*f)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log(2*(2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e)) - 75*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 75*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(14*cos(f*x + e)^4 - 14*cos(f*x + e)^2 - (29*cos(f*x + e)^3 - 21*cos(f*x + e))*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 24*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - sqrt(2))/f^4 + 24*8^(1/4)*sqrt(2)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(1/16*8^(3/4)*sqrt(2)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 8^(1/4)*(sqrt(2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + 2*cos(f*x + e) + 2*sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 1/8*8^(3/4)*(2*f^5*sqrt(f^(-4)) + sqrt(2)*f^3)*sqrt(-2*sqrt(2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + sqrt(2))/f^4)/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
400,1,1008,0,0.500907," ","integrate(tan(f*x+e)^5/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{420 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) \cos\left(f x + e\right)^{3} + 420 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right) \cos\left(f x + e\right)^{3} + 105 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 105 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 8 \, {\left(40 \, \cos\left(f x + e\right)^{3} - {\left(26 \, \cos\left(f x + e\right)^{2} - 15\right)} \sin\left(f x + e\right) - 18 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{420 \, f \cos\left(f x + e\right)^{3}}"," ",0,"-1/420*(420*(1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))*cos(f*x + e)^3 + 420*(1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))*cos(f*x + e)^3 + 105*(1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e)^3 + f*cos(f*x + e)^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 105*(1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e)^3 + f*cos(f*x + e)^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 8*(40*cos(f*x + e)^3 - (26*cos(f*x + e)^2 - 15)*sin(f*x + e) - 18*cos(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^3)","B",0
401,1,974,0,0.576599," ","integrate(tan(f*x+e)^3/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{12 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) \cos\left(f x + e\right) + 12 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right) \cos\left(f x + e\right) + 3 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 3 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 8 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} {\left(2 \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)}}{12 \, f \cos\left(f x + e\right)}"," ",0,"1/12*(12*(1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))*cos(f*x + e) + 12*(1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))*cos(f*x + e) + 3*(1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 3*(1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 8*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(2*cos(f*x + e) - sin(f*x + e)))/(f*cos(f*x + e))","B",0
402,1,878,0,0.675934," ","integrate(tan(f*x+e)/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + \frac{1}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) - \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right)"," ",0,"-1/4*(1/2)^(1/4)*(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1/4*(1/2)^(1/4)*(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - (1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2)) - (1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))","B",0
403,1,942,0,0.843071," ","integrate(cot(f*x+e)/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) + 4 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} + f\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} + f\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 4 \, \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 4 \, \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right)}{4 \, f}"," ",0,"1/4*(4*(1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2)) + 4*(1/2)^(3/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2)) + (1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4)) + f)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - (1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4)) + f)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 4*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 4*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1))/f","B",0
404,1,1121,0,0.869289," ","integrate(cot(f*x+e)^3/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(f \cos\left(f x + e\right)^{2} + \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} {\left(f \cos\left(f x + e\right)^{2} + \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 5 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 5 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(2 \, \cos\left(f x + e\right)^{2} - 3 \, \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \frac{8 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}} + \frac{8 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}}}{8 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"-1/8*(2*(1/2)^(1/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f*cos(f*x + e)^2 + sqrt(1/2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - f)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 2*(1/2)^(1/4)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f*cos(f*x + e)^2 + sqrt(1/2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - f)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 5*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 5*(cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(2*cos(f*x + e)^2 - 3*cos(f*x + e)*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 8*(1/2)^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))/f^4 + 8*(1/2)^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))/f^4)/(f*cos(f*x + e)^2 - f)","B",0
405,1,1235,0,0.703654," ","integrate(cot(f*x+e)^5/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{96 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + f\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 96 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + f\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 345 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 345 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(74 \, \cos\left(f x + e\right)^{4} - 26 \, \cos\left(f x + e\right)^{2} - {\left(95 \, \cos\left(f x + e\right)^{3} - 39 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \frac{384 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}} + \frac{384 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(2 \, \sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + f \cos\left(f x + e\right)\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \sqrt{\frac{1}{f^{4}}} + \sqrt{\frac{1}{2}} f^{3}\right)} \sqrt{-4 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 4} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}}}{384 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"1/384*(96*(1/2)^(1/4)*(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + sqrt(1/2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + f)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 96*(1/2)^(1/4)*(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + sqrt(1/2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + f)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 345*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 345*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(74*cos(f*x + e)^4 - 26*cos(f*x + e)^2 - (95*cos(f*x + e)^3 - 39*cos(f*x + e))*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 384*(1/2)^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))/f^4 + 384*(1/2)^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*(f^(-4))^(1/4)*arctan(2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - (1/2)^(1/4)*(2*sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e) + f*cos(f*x + e))*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(3/4)*(f^5*sqrt(f^(-4)) + sqrt(1/2)*f^3)*sqrt(-4*sqrt(1/2)*f^2*sqrt(f^(-4)) + 4)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))/f^4)/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
406,1,847,0,0.997729," ","integrate(tan(f*x+e)^4/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{60 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) \cos\left(f x + e\right)^{2} + 60 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right) \cos\left(f x + e\right)^{2} + 15 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{2} - f \cos\left(f x + e\right)^{2}\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 15 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right)^{2} - f \cos\left(f x + e\right)^{2}\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, {\left(10 \, \cos\left(f x + e\right)^{2} + 4 \, \cos\left(f x + e\right) \sin\left(f x + e\right) - 3\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{30 \, f \cos\left(f x + e\right)^{2}}"," ",0,"-1/30*(60*(1/2)^(3/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))*cos(f*x + e)^2 + 60*(1/2)^(3/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))*cos(f*x + e)^2 + 15*(1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e)^2 - f*cos(f*x + e)^2)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 15*(1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4))*cos(f*x + e)^2 - f*cos(f*x + e)^2)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 4*(10*cos(f*x + e)^2 + 4*cos(f*x + e)*sin(f*x + e) - 3)*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/(f*cos(f*x + e)^2)","B",0
407,1,764,0,0.585773," ","integrate(tan(f*x+e)^2/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) + 4 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right) + \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} - f\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(\sqrt{\frac{1}{2}} f^{3} \sqrt{\frac{1}{f^{4}}} - f\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 4 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{2 \, f}"," ",0,"1/2*(4*(1/2)^(3/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2)) + 4*(1/2)^(3/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2)) + (1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4)) - f)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - (1/2)^(1/4)*(sqrt(1/2)*f^3*sqrt(f^(-4)) - f)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 4*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)))/f","B",0
408,1,728,0,0.553600," ","integrate(1/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} {\left(\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} - 1\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + \frac{1}{2} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} {\left(\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} - 1\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right)"," ",0,"-1/2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(sqrt(1/2)*f^2*sqrt(f^(-4)) - 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1/2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(sqrt(1/2)*f^2*sqrt(f^(-4)) - 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 2*(1/2)^(3/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2)) - 2*(1/2)^(3/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))","B",0
409,1,958,0,0.646401," ","integrate(cot(f*x+e)^2/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{\left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} {\left(f \cos\left(f x + e\right)^{2} - \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} {\left(f \cos\left(f x + e\right)^{2} - \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{2} - f^{3}\right)} \sqrt{\frac{1}{f^{4}}} - f\right)} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 2 \, \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{2} - f^{5}\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}}}{2 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"-1/2*((1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f*cos(f*x + e)^2 - sqrt(1/2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - f)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - (1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f*cos(f*x + e)^2 - sqrt(1/2)*(f^3*cos(f*x + e)^2 - f^3)*sqrt(f^(-4)) - f)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 2*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + (cos(f*x + e)^2 - 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 4*(1/2)^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))/f^4 - 4*(1/2)^(3/4)*(f^5*cos(f*x + e)^2 - f^5)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))/f^4)/(f*cos(f*x + e)^2 - f)","B",0
410,1,1086,0,0.579293," ","integrate(cot(f*x+e)^4/(1+tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{24 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} - \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + f\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 24 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} - \sqrt{\frac{1}{2}} {\left(f^{3} \cos\left(f x + e\right)^{4} - 2 \, f^{3} \cos\left(f x + e\right)^{2} + f^{3}\right)} \sqrt{\frac{1}{f^{4}}} + f\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 9 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + 1\right) + 9 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \log\left(\sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - 1\right) - 2 \, {\left(10 \, \cos\left(f x + e\right)^{4} - 10 \, \cos\left(f x + e\right)^{2} + {\left(17 \, \cos\left(f x + e\right)^{3} - 9 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \frac{96 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - f^{2} \sqrt{\frac{1}{f^{4}}} - 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}} - \frac{96 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(f^{5} \cos\left(f x + e\right)^{4} - 2 \, f^{5} \cos\left(f x + e\right)^{2} + f^{5}\right)} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} \frac{1}{f^{4}}^{\frac{1}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{2 \, \sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} \cos\left(f x + e\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{1}{4}} \cos\left(f x + e\right) + \cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{\sqrt{\frac{1}{2}} f^{2} \sqrt{\frac{1}{f^{4}}} + 1} f^{3} \sqrt{\frac{\cos\left(f x + e\right) + \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \frac{1}{f^{4}}^{\frac{3}{4}} + f^{2} \sqrt{\frac{1}{f^{4}}} + 2 \, \sqrt{\frac{1}{2}}\right)}{f^{4}}}{48 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"1/48*(24*(1/2)^(1/4)*(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 - sqrt(1/2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + f)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 24*(1/2)^(1/4)*(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 - sqrt(1/2)*(f^3*cos(f*x + e)^4 - 2*f^3*cos(f*x + e)^2 + f^3)*sqrt(f^(-4)) + f)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*log((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 9*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) + 1) + 9*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*log(sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 1) - 2*(10*cos(f*x + e)^4 - 10*cos(f*x + e)^2 + (17*cos(f*x + e)^3 - 9*cos(f*x + e))*sin(f*x + e))*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e)) - 96*(1/2)^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) + 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - f^2*sqrt(f^(-4)) - 2*sqrt(1/2))/f^4 - 96*(1/2)^(3/4)*(f^5*cos(f*x + e)^4 - 2*f^5*cos(f*x + e)^2 + f^5)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*(f^(-4))^(1/4)*arctan(2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((2*sqrt(1/2)*f^2*sqrt(f^(-4))*cos(f*x + e) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(1/4)*cos(f*x + e) + cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) - 2*(1/2)^(1/4)*sqrt(sqrt(1/2)*f^2*sqrt(f^(-4)) + 1)*f^3*sqrt((cos(f*x + e) + sin(f*x + e))/cos(f*x + e))*(f^(-4))^(3/4) + f^2*sqrt(f^(-4)) + 2*sqrt(1/2))/f^4)/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
411,0,0,0,0.489604," ","integrate((d*tan(f*x+e))^n*(a+a*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \tan\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*tan(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
412,1,80,0,0.444218," ","integrate(tan(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, b \tan\left(d x + c\right)^{5} + 15 \, a \tan\left(d x + c\right)^{4} - 20 \, b \tan\left(d x + c\right)^{3} - 60 \, b d x - 30 \, a \tan\left(d x + c\right)^{2} - 30 \, a \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 60 \, b \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b*tan(d*x + c)^5 + 15*a*tan(d*x + c)^4 - 20*b*tan(d*x + c)^3 - 60*b*d*x - 30*a*tan(d*x + c)^2 - 30*a*log(1/(tan(d*x + c)^2 + 1)) + 60*b*tan(d*x + c))/d","A",0
413,1,69,0,0.462548," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b \tan\left(d x + c\right)^{4} + 4 \, a \tan\left(d x + c\right)^{3} + 12 \, a d x - 6 \, b \tan\left(d x + c\right)^{2} - 6 \, b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b*tan(d*x + c)^4 + 4*a*tan(d*x + c)^3 + 12*a*d*x - 6*b*tan(d*x + c)^2 - 6*b*log(1/(tan(d*x + c)^2 + 1)) - 12*a*tan(d*x + c))/d","A",0
414,1,58,0,0.491455," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b \tan\left(d x + c\right)^{3} + 6 \, b d x + 3 \, a \tan\left(d x + c\right)^{2} + 3 \, a \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 6 \, b \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*b*tan(d*x + c)^3 + 6*b*d*x + 3*a*tan(d*x + c)^2 + 3*a*log(1/(tan(d*x + c)^2 + 1)) - 6*b*tan(d*x + c))/d","A",0
415,1,47,0,0.555066," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d x - b \tan\left(d x + c\right)^{2} - b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*a*d*x - b*tan(d*x + c)^2 - b*log(1/(tan(d*x + c)^2 + 1)) - 2*a*tan(d*x + c))/d","A",0
416,1,35,0,0.462433," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b d x + a \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, b \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*b*d*x + a*log(1/(tan(d*x + c)^2 + 1)) - 2*b*tan(d*x + c))/d","A",0
417,1,27,0,0.479233," ","integrate(a+b*tan(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a d x - b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*a*d*x - b*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
418,1,35,0,0.484066," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b d x + a \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(2*b*d*x + a*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)))/d","B",0
419,1,59,0,0.470126," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d x \tan\left(d x + c\right) - b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + 2 \, a}{2 \, d \tan\left(d x + c\right)}"," ",0,"-1/2*(2*a*d*x*tan(d*x + c) - b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*a)/(d*tan(d*x + c))","B",0
420,1,72,0,0.522655," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{a \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + {\left(2 \, b d x + a\right)} \tan\left(d x + c\right)^{2} + 2 \, b \tan\left(d x + c\right) + a}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(a*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (2*b*d*x + a)*tan(d*x + c)^2 + 2*b*tan(d*x + c) + a)/(d*tan(d*x + c)^2)","A",0
421,1,89,0,0.479624," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} - 3 \, {\left(2 \, a d x - b\right)} \tan\left(d x + c\right)^{3} - 6 \, a \tan\left(d x + c\right)^{2} + 3 \, b \tan\left(d x + c\right) + 2 \, a}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 - 3*(2*a*d*x - b)*tan(d*x + c)^3 - 6*a*tan(d*x + c)^2 + 3*b*tan(d*x + c) + 2*a)/(d*tan(d*x + c)^3)","A",0
422,1,100,0,0.471020," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, a \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + 3 \, {\left(4 \, b d x + 3 \, a\right)} \tan\left(d x + c\right)^{4} + 12 \, b \tan\left(d x + c\right)^{3} + 6 \, a \tan\left(d x + c\right)^{2} - 4 \, b \tan\left(d x + c\right) - 3 \, a}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*a*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*(4*b*d*x + 3*a)*tan(d*x + c)^4 + 12*b*tan(d*x + c)^3 + 6*a*tan(d*x + c)^2 - 4*b*tan(d*x + c) - 3*a)/(d*tan(d*x + c)^4)","A",0
423,1,111,0,0.613347," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{5} - 15 \, {\left(4 \, a d x - 3 \, b\right)} \tan\left(d x + c\right)^{5} - 60 \, a \tan\left(d x + c\right)^{4} + 30 \, b \tan\left(d x + c\right)^{3} + 20 \, a \tan\left(d x + c\right)^{2} - 15 \, b \tan\left(d x + c\right) - 12 \, a}{60 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/60*(30*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 - 15*(4*a*d*x - 3*b)*tan(d*x + c)^5 - 60*a*tan(d*x + c)^4 + 30*b*tan(d*x + c)^3 + 20*a*tan(d*x + c)^2 - 15*b*tan(d*x + c) - 12*a)/(d*tan(d*x + c)^5)","A",0
424,1,109,0,0.483483," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, b^{2} \tan\left(d x + c\right)^{5} + 15 \, a b \tan\left(d x + c\right)^{4} - 30 \, a b \tan\left(d x + c\right)^{2} + 10 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(a^{2} - b^{2}\right)} d x - 30 \, a b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 30 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(6*b^2*tan(d*x + c)^5 + 15*a*b*tan(d*x + c)^4 - 30*a*b*tan(d*x + c)^2 + 10*(a^2 - b^2)*tan(d*x + c)^3 + 30*(a^2 - b^2)*d*x - 30*a*b*log(1/(tan(d*x + c)^2 + 1)) - 30*(a^2 - b^2)*tan(d*x + c))/d","A",0
425,1,90,0,0.479465," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \tan\left(d x + c\right)^{4} + 8 \, a b \tan\left(d x + c\right)^{3} + 24 \, a b d x - 24 \, a b \tan\left(d x + c\right) + 6 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(a^{2} - b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{12 \, d}"," ",0,"1/12*(3*b^2*tan(d*x + c)^4 + 8*a*b*tan(d*x + c)^3 + 24*a*b*d*x - 24*a*b*tan(d*x + c) + 6*(a^2 - b^2)*tan(d*x + c)^2 + 6*(a^2 - b^2)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
426,1,77,0,0.481580," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{b^{2} \tan\left(d x + c\right)^{3} + 3 \, a b \tan\left(d x + c\right)^{2} - 3 \, {\left(a^{2} - b^{2}\right)} d x + 3 \, a b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 3 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(b^2*tan(d*x + c)^3 + 3*a*b*tan(d*x + c)^2 - 3*(a^2 - b^2)*d*x + 3*a*b*log(1/(tan(d*x + c)^2 + 1)) + 3*(a^2 - b^2)*tan(d*x + c))/d","A",0
427,1,58,0,0.470323," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a b d x - b^{2} \tan\left(d x + c\right)^{2} - 4 \, a b \tan\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"-1/2*(4*a*b*d*x - b^2*tan(d*x + c)^2 - 4*a*b*tan(d*x + c) + (a^2 - b^2)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
428,1,44,0,0.464715," ","integrate((a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d x - a b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + b^{2} \tan\left(d x + c\right)}{d}"," ",0,"((a^2 - b^2)*d*x - a*b*log(1/(tan(d*x + c)^2 + 1)) + b^2*tan(d*x + c))/d","A",0
429,1,56,0,0.486780," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a b d x + a^{2} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - b^{2} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(4*a*b*d*x + a^2*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - b^2*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
430,1,67,0,0.459017," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - b^{2}\right)} d x \tan\left(d x + c\right) - a b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + a^{2}}{d \tan\left(d x + c\right)}"," ",0,"-((a^2 - b^2)*d*x*tan(d*x + c) - a*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) + a^2)/(d*tan(d*x + c))","A",0
431,1,86,0,0.496228," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + 4 \, a b \tan\left(d x + c\right) + {\left(4 \, a b d x + a^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2}}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*((a^2 - b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + 4*a*b*tan(d*x + c) + (4*a*b*d*x + a^2)*tan(d*x + c)^2 + a^2)/(d*tan(d*x + c)^2)","A",0
432,1,107,0,0.480913," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{2} - b^{2}\right)} d x - a b\right)} \tan\left(d x + c\right)^{3} + 3 \, a b \tan\left(d x + c\right) - 3 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2}}{3 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*a*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 - 3*((a^2 - b^2)*d*x - a*b)*tan(d*x + c)^3 + 3*a*b*tan(d*x + c) - 3*(a^2 - b^2)*tan(d*x + c)^2 + a^2)/(d*tan(d*x + c)^3)","A",0
433,1,128,0,0.453458," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{2} - b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + 24 \, a b \tan\left(d x + c\right)^{3} + 3 \, {\left(8 \, a b d x + 3 \, a^{2} - 2 \, b^{2}\right)} \tan\left(d x + c\right)^{4} - 8 \, a b \tan\left(d x + c\right) + 6 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 3 \, a^{2}}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(a^2 - b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 24*a*b*tan(d*x + c)^3 + 3*(8*a*b*d*x + 3*a^2 - 2*b^2)*tan(d*x + c)^4 - 8*a*b*tan(d*x + c) + 6*(a^2 - b^2)*tan(d*x + c)^2 - 3*a^2)/(d*tan(d*x + c)^4)","A",0
434,1,141,0,0.515626," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 \, a b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{5} - 15 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - 3 \, a b\right)} \tan\left(d x + c\right)^{5} + 30 \, a b \tan\left(d x + c\right)^{3} - 30 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{4} - 15 \, a b \tan\left(d x + c\right) + 10 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 6 \, a^{2}}{30 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/30*(30*a*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 - 15*(2*(a^2 - b^2)*d*x - 3*a*b)*tan(d*x + c)^5 + 30*a*b*tan(d*x + c)^3 - 30*(a^2 - b^2)*tan(d*x + c)^4 - 15*a*b*tan(d*x + c) + 10*(a^2 - b^2)*tan(d*x + c)^2 - 6*a^2)/(d*tan(d*x + c)^5)","A",0
435,1,136,0,0.461966," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, b^{3} \tan\left(d x + c\right)^{5} + 45 \, a b^{2} \tan\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} + 60 \, {\left(3 \, a^{2} b - b^{3}\right)} d x + 30 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2} + 30 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 60 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b^3*tan(d*x + c)^5 + 45*a*b^2*tan(d*x + c)^4 + 20*(3*a^2*b - b^3)*tan(d*x + c)^3 + 60*(3*a^2*b - b^3)*d*x + 30*(a^3 - 3*a*b^2)*tan(d*x + c)^2 + 30*(a^3 - 3*a*b^2)*log(1/(tan(d*x + c)^2 + 1)) - 60*(3*a^2*b - b^3)*tan(d*x + c))/d","A",0
436,1,113,0,0.471487," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} \tan\left(d x + c\right)^{4} + 4 \, a b^{2} \tan\left(d x + c\right)^{3} - 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} d x + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(b^3*tan(d*x + c)^4 + 4*a*b^2*tan(d*x + c)^3 - 4*(a^3 - 3*a*b^2)*d*x + 2*(3*a^2*b - b^3)*tan(d*x + c)^2 + 2*(3*a^2*b - b^3)*log(1/(tan(d*x + c)^2 + 1)) + 4*(a^3 - 3*a*b^2)*tan(d*x + c))/d","A",0
437,1,94,0,0.457973," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} \tan\left(d x + c\right)^{3} + 9 \, a b^{2} \tan\left(d x + c\right)^{2} - 6 \, {\left(3 \, a^{2} b - b^{3}\right)} d x - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*b^3*tan(d*x + c)^3 + 9*a*b^2*tan(d*x + c)^2 - 6*(3*a^2*b - b^3)*d*x - 3*(a^3 - 3*a*b^2)*log(1/(tan(d*x + c)^2 + 1)) + 6*(3*a^2*b - b^3)*tan(d*x + c))/d","A",0
438,1,71,0,0.477682," ","integrate((a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} \tan\left(d x + c\right)^{2} + 6 \, a b^{2} \tan\left(d x + c\right) + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d x - {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(b^3*tan(d*x + c)^2 + 6*a*b^2*tan(d*x + c) + 2*(a^3 - 3*a*b^2)*d*x - (3*a^2*b - b^3)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
439,1,78,0,0.656487," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, a b^{2} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, b^{3} \tan\left(d x + c\right) + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} d x}{2 \, d}"," ",0,"1/2*(a^3*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - 3*a*b^2*log(1/(tan(d*x + c)^2 + 1)) + 2*b^3*tan(d*x + c) + 2*(3*a^2*b - b^3)*d*x)/d","A",0
440,1,97,0,0.469751," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) - b^{3} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d x \tan\left(d x + c\right) - 2 \, a^{3}}{2 \, d \tan\left(d x + c\right)}"," ",0,"1/2*(3*a^2*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) - b^3*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c) - 2*(a^3 - 3*a*b^2)*d*x*tan(d*x + c) - 2*a^3)/(d*tan(d*x + c))","A",0
441,1,99,0,0.445295," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, a^{2} b \tan\left(d x + c\right) + {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + a^{3} + {\left(a^{3} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2}}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(6*a^2*b*tan(d*x + c) + (a^3 - 3*a*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + a^3 + (a^3 + 2*(3*a^2*b - b^3)*d*x)*tan(d*x + c)^2)/(d*tan(d*x + c)^2)","A",0
442,1,126,0,0.429106," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} + 9 \, a^{2} b \tan\left(d x + c\right) + 3 \, {\left(3 \, a^{2} b - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 2 \, a^{3} - 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{6 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*(3*a^2*b - b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 9*a^2*b*tan(d*x + c) + 3*(3*a^2*b - 2*(a^3 - 3*a*b^2)*d*x)*tan(d*x + c)^3 + 2*a^3 - 6*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^3)","A",0
443,1,152,0,0.600051," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + {\left(3 \, a^{3} - 6 \, a b^{2} + 4 \, {\left(3 \, a^{2} b - b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{4} - 4 \, a^{2} b \tan\left(d x + c\right) + 4 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} - a^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{4 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/4*(2*(a^3 - 3*a*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + (3*a^3 - 6*a*b^2 + 4*(3*a^2*b - b^3)*d*x)*tan(d*x + c)^4 - 4*a^2*b*tan(d*x + c) + 4*(3*a^2*b - b^3)*tan(d*x + c)^3 - a^3 + 2*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^4)","A",0
444,1,173,0,0.432524," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{30 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{5} + 15 \, {\left(9 \, a^{2} b - 2 \, b^{3} - 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} d x\right)} \tan\left(d x + c\right)^{5} - 60 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{4} - 45 \, a^{2} b \tan\left(d x + c\right) + 30 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} - 12 \, a^{3} + 20 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{60 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/60*(30*(3*a^2*b - b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 + 15*(9*a^2*b - 2*b^3 - 4*(a^3 - 3*a*b^2)*d*x)*tan(d*x + c)^5 - 60*(a^3 - 3*a*b^2)*tan(d*x + c)^4 - 45*a^2*b*tan(d*x + c) + 30*(3*a^2*b - b^3)*tan(d*x + c)^3 - 12*a^3 + 20*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^5)","A",0
445,1,170,0,0.462700," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{10 \, b^{4} \tan\left(d x + c\right)^{6} + 48 \, a b^{3} \tan\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{4} + 80 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} + 240 \, {\left(a^{3} b - a b^{3}\right)} d x + 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{2} + 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 240 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*b^4*tan(d*x + c)^6 + 48*a*b^3*tan(d*x + c)^5 + 15*(6*a^2*b^2 - b^4)*tan(d*x + c)^4 + 80*(a^3*b - a*b^3)*tan(d*x + c)^3 + 240*(a^3*b - a*b^3)*d*x + 30*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c)^2 + 30*(a^4 - 6*a^2*b^2 + b^4)*log(1/(tan(d*x + c)^2 + 1)) - 240*(a^3*b - a*b^3)*tan(d*x + c))/d","A",0
446,1,148,0,0.427498," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} \tan\left(d x + c\right)^{5} + 15 \, a b^{3} \tan\left(d x + c\right)^{4} + 5 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{3} - 15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d x + 30 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{2} + 30 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*b^4*tan(d*x + c)^5 + 15*a*b^3*tan(d*x + c)^4 + 5*(6*a^2*b^2 - b^4)*tan(d*x + c)^3 - 15*(a^4 - 6*a^2*b^2 + b^4)*d*x + 30*(a^3*b - a*b^3)*tan(d*x + c)^2 + 30*(a^3*b - a*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 15*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c))/d","A",0
447,1,123,0,0.436103," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} \tan\left(d x + c\right)^{4} + 16 \, a b^{3} \tan\left(d x + c\right)^{3} - 48 \, {\left(a^{3} b - a b^{3}\right)} d x + 6 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 48 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b^4*tan(d*x + c)^4 + 16*a*b^3*tan(d*x + c)^3 - 48*(a^3*b - a*b^3)*d*x + 6*(6*a^2*b^2 - b^4)*tan(d*x + c)^2 - 6*(a^4 - 6*a^2*b^2 + b^4)*log(1/(tan(d*x + c)^2 + 1)) + 48*(a^3*b - a*b^3)*tan(d*x + c))/d","A",0
448,1,100,0,0.428082," ","integrate((a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{b^{4} \tan\left(d x + c\right)^{3} + 6 \, a b^{3} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d x - 6 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 3 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(b^4*tan(d*x + c)^3 + 6*a*b^3*tan(d*x + c)^2 + 3*(a^4 - 6*a^2*b^2 + b^4)*d*x - 6*(a^3*b - a*b^3)*log(1/(tan(d*x + c)^2 + 1)) + 3*(6*a^2*b^2 - b^4)*tan(d*x + c))/d","A",0
449,1,101,0,0.519454," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{b^{4} \tan\left(d x + c\right)^{2} + a^{4} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 8 \, a b^{3} \tan\left(d x + c\right) + 8 \, {\left(a^{3} b - a b^{3}\right)} d x - {\left(6 \, a^{2} b^{2} - b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(b^4*tan(d*x + c)^2 + a^4*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + 8*a*b^3*tan(d*x + c) + 8*(a^3*b - a*b^3)*d*x - (6*a^2*b^2 - b^4)*log(1/(tan(d*x + c)^2 + 1)))/d","A",0
450,1,114,0,0.543543," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{2 \, a^{3} b \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) - 2 \, a b^{3} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + b^{4} \tan\left(d x + c\right)^{2} - a^{4} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d x \tan\left(d x + c\right)}{d \tan\left(d x + c\right)}"," ",0,"(2*a^3*b*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c) - 2*a*b^3*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c) + b^4*tan(d*x + c)^2 - a^4 - (a^4 - 6*a^2*b^2 + b^4)*d*x*tan(d*x + c))/(d*tan(d*x + c))","A",0
451,1,126,0,0.459292," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{b^{4} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + 8 \, a^{3} b \tan\left(d x + c\right) + a^{4} + {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + {\left(a^{4} + 8 \, {\left(a^{3} b - a b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2}}{2 \, d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(b^4*log(1/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + 8*a^3*b*tan(d*x + c) + a^4 + (a^4 - 6*a^2*b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + (a^4 + 8*(a^3*b - a*b^3)*d*x)*tan(d*x + c)^2)/(d*tan(d*x + c)^2)","A",0
452,1,131,0,0.466626," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, a^{3} b \tan\left(d x + c\right) + 6 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} + a^{4} + 3 \, {\left(2 \, a^{3} b - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{3 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/3*(6*a^3*b*tan(d*x + c) + 6*(a^3*b - a*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + a^4 + 3*(2*a^3*b - (a^4 - 6*a^2*b^2 + b^4)*d*x)*tan(d*x + c)^3 - 3*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^3)","A",0
453,1,162,0,0.474246," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} - 16 \, a^{3} b \tan\left(d x + c\right) + 3 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 16 \, {\left(a^{3} b - a b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{4} - 3 \, a^{4} + 48 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{12 \, d \tan\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 - 16*a^3*b*tan(d*x + c) + 3*(3*a^4 - 12*a^2*b^2 + 16*(a^3*b - a*b^3)*d*x)*tan(d*x + c)^4 - 3*a^4 + 48*(a^3*b - a*b^3)*tan(d*x + c)^3 + 6*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^4)","A",0
454,1,186,0,0.484169," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{30 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{5} + 15 \, {\left(3 \, a^{3} b - 2 \, a b^{3} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{5} - 15 \, a^{3} b \tan\left(d x + c\right) - 15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} - 3 \, a^{4} + 30 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} + 5 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{15 \, d \tan\left(d x + c\right)^{5}}"," ",0,"1/15*(30*(a^3*b - a*b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^5 + 15*(3*a^3*b - 2*a*b^3 - (a^4 - 6*a^2*b^2 + b^4)*d*x)*tan(d*x + c)^5 - 15*a^3*b*tan(d*x + c) - 15*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c)^4 - 3*a^4 + 30*(a^3*b - a*b^3)*tan(d*x + c)^3 + 5*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^5)","A",0
455,1,214,0,0.481597," ","integrate(cot(d*x+c)^7*(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{4} - 54 \, a^{2} b^{2} + 6 \, b^{4} + 48 \, {\left(a^{3} b - a b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{6} + 240 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{5} + 48 \, a^{3} b \tan\left(d x + c\right) + 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} + 10 \, a^{4} - 80 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} - 15 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{60 \, d \tan\left(d x + c\right)^{6}}"," ",0,"-1/60*(30*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^6 + 5*(11*a^4 - 54*a^2*b^2 + 6*b^4 + 48*(a^3*b - a*b^3)*d*x)*tan(d*x + c)^6 + 240*(a^3*b - a*b^3)*tan(d*x + c)^5 + 48*a^3*b*tan(d*x + c) + 30*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c)^4 + 10*a^4 - 80*(a^3*b - a*b^3)*tan(d*x + c)^3 - 15*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/(d*tan(d*x + c)^6)","A",0
456,1,181,0,0.508961," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, a b^{5} d x - 6 \, a^{6} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(a^{4} b^{2} - b^{6}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(a^{6} + b^{6}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 12 \, {\left(a^{5} b - a b^{5}\right)} \tan\left(d x + c\right)}{12 \, {\left(a^{2} b^{5} + b^{7}\right)} d}"," ",0,"-1/12*(12*a*b^5*d*x - 6*a^6*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(a^2*b^4 + b^6)*tan(d*x + c)^4 + 4*(a^3*b^3 + a*b^5)*tan(d*x + c)^3 - 6*(a^4*b^2 - b^6)*tan(d*x + c)^2 + 6*(a^6 + b^6)*log(1/(tan(d*x + c)^2 + 1)) + 12*(a^5*b - a*b^5)*tan(d*x + c))/((a^2*b^5 + b^7)*d)","A",0
457,1,159,0,0.484054," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, b^{5} d x - 3 \, a^{5} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{5} - a b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 6 \, {\left(a^{4} b - b^{5}\right)} \tan\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/6*(6*b^5*d*x - 3*a^5*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 2*(a^2*b^3 + b^5)*tan(d*x + c)^3 - 3*(a^3*b^2 + a*b^4)*tan(d*x + c)^2 + 3*(a^5 - a*b^4)*log(1/(tan(d*x + c)^2 + 1)) + 6*(a^4*b - b^5)*tan(d*x + c))/((a^2*b^4 + b^6)*d)","A",0
458,1,134,0,0.517262," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a b^{3} d x + a^{4} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{2} - {\left(a^{4} - b^{4}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} + b^{5}\right)} d}"," ",0,"1/2*(2*a*b^3*d*x + a^4*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (a^2*b^2 + b^4)*tan(d*x + c)^2 - (a^4 - b^4)*log(1/(tan(d*x + c)^2 + 1)) - 2*(a^3*b + a*b^3)*tan(d*x + c))/((a^2*b^3 + b^5)*d)","A",0
459,1,111,0,0.456147," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d x + a^{3} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(a^{3} + a b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} + b^{4}\right)} d}"," ",0,"-1/2*(2*b^3*d*x + a^3*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (a^3 + a*b^2)*log(1/(tan(d*x + c)^2 + 1)) - 2*(a^2*b + b^3)*tan(d*x + c))/((a^2*b^2 + b^4)*d)","A",0
460,1,89,0,0.445982," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b d x - a^{2} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(a^{2} + b^{2}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{2} b + b^{3}\right)} d}"," ",0,"-1/2*(2*a*b*d*x - a^2*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (a^2 + b^2)*log(1/(tan(d*x + c)^2 + 1)))/((a^2*b + b^3)*d)","A",0
461,1,63,0,0.459175," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b d x - a \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/2*(2*b*d*x - a*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)))/((a^2 + b^2)*d)","A",0
462,1,62,0,0.427921," ","integrate(1/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d x + b \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/2*(2*a*d*x + b*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)))/((a^2 + b^2)*d)","A",0
463,1,98,0,0.491746," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b d x + b^{2} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(a^{2} + b^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, {\left(a^{3} + a b^{2}\right)} d}"," ",0,"-1/2*(2*a*b*d*x + b^2*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (a^2 + b^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)))/((a^3 + a*b^2)*d)","A",0
464,1,140,0,0.497295," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{3} d x \tan\left(d x + c\right) - b^{3} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right) + 2 \, a^{3} + 2 \, a b^{2} + {\left(a^{2} b + b^{3}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)}{2 \, {\left(a^{4} + a^{2} b^{2}\right)} d \tan\left(d x + c\right)}"," ",0,"-1/2*(2*a^3*d*x*tan(d*x + c) - b^3*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1))*tan(d*x + c) + 2*a^3 + 2*a*b^2 + (a^2*b + b^3)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c))/((a^4 + a^2*b^2)*d*tan(d*x + c))","A",0
465,1,180,0,0.484437," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{4} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + a^{4} + a^{2} b^{2} + {\left(a^{4} - b^{4}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} - {\left(2 \, a^{3} b d x - a^{4} - a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \tan\left(d x + c\right)^{2}}"," ",0,"-1/2*(b^4*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + a^4 + a^2*b^2 + (a^4 - b^4)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 - (2*a^3*b*d*x - a^4 - a^2*b^2)*tan(d*x + c)^2 - 2*(a^3*b + a*b^3)*tan(d*x + c))/((a^5 + a^3*b^2)*d*tan(d*x + c)^2)","A",0
466,1,207,0,0.482785," ","integrate(cot(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b^{5} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} - 2 \, a^{5} - 2 \, a^{3} b^{2} + 3 \, {\left(a^{4} b - b^{5}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} d x + a^{4} b + a^{2} b^{3}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(a^{5} - a b^{4}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} \tan\left(d x + c\right)}{6 \, {\left(a^{6} + a^{4} b^{2}\right)} d \tan\left(d x + c\right)^{3}}"," ",0,"1/6*(3*b^5*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 - 2*a^5 - 2*a^3*b^2 + 3*(a^4*b - b^5)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^3 + 3*(2*a^5*d*x + a^4*b + a^2*b^3)*tan(d*x + c)^3 + 6*(a^5 - a*b^4)*tan(d*x + c)^2 + 3*(a^4*b + a^2*b^3)*tan(d*x + c))/((a^6 + a^4*b^2)*d*tan(d*x + c)^3)","A",0
467,1,387,0,0.739228," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b^{5} - a b^{7}\right)} d x - 3 \, {\left(2 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{8} + 3 \, a^{6} b^{2} + {\left(2 \, a^{7} b + 3 \, a^{5} b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(2 \, a^{8} + 3 \, a^{6} b^{2} - a^{2} b^{6} + {\left(2 \, a^{7} b + 3 \, a^{5} b^{3} - a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(4 \, a^{7} b + 4 \, a^{5} b^{3} - a^{3} b^{5} - 2 \, a b^{7} - {\left(a^{2} b^{6} - b^{8}\right)} d x\right)} \tan\left(d x + c\right)}{3 \, {\left({\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} d \tan\left(d x + c\right) + {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}"," ",0,"-1/3*(6*a^6*b^2 + 6*a^4*b^4 + 3*a^2*b^6 - (a^4*b^4 + 2*a^2*b^6 + b^8)*tan(d*x + c)^4 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*tan(d*x + c)^3 + 3*(a^3*b^5 - a*b^7)*d*x - 3*(2*a^6*b^2 + 3*a^4*b^4 - b^8)*tan(d*x + c)^2 + 3*(2*a^8 + 3*a^6*b^2 + (2*a^7*b + 3*a^5*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(2*a^8 + 3*a^6*b^2 - a^2*b^6 + (2*a^7*b + 3*a^5*b^3 - a*b^7)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 3*(4*a^7*b + 4*a^5*b^3 - a^3*b^5 - 2*a*b^7 - (a^2*b^6 - b^8)*d*x)*tan(d*x + c))/((a^4*b^6 + 2*a^2*b^8 + b^10)*d*tan(d*x + c) + (a^5*b^5 + 2*a^3*b^7 + a*b^9)*d)","A",0
468,1,340,0,0.496737," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{5} d x + 3 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{3} - 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 5 \, a^{5} b^{2} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(3 \, a^{7} + 5 \, a^{5} b^{2} + a^{3} b^{4} - a b^{6} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(4 \, a b^{6} d x - 6 \, a^{6} b - 7 \, a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d\right)}}"," ",0,"1/2*(4*a^2*b^5*d*x + 3*a^5*b^2 + 2*a^3*b^4 + a*b^6 + (a^4*b^3 + 2*a^2*b^5 + b^7)*tan(d*x + c)^3 - 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*tan(d*x + c)^2 + (3*a^7 + 5*a^5*b^2 + (3*a^6*b + 5*a^4*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (3*a^7 + 5*a^5*b^2 + a^3*b^4 - a*b^6 + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) + (4*a*b^6*d*x - 6*a^6*b - 7*a^4*b^3 - 2*a^2*b^5 + b^7)*tan(d*x + c))/((a^4*b^5 + 2*a^2*b^7 + b^9)*d*tan(d*x + c) + (a^5*b^4 + 2*a^3*b^6 + a*b^8)*d)","A",0
469,1,288,0,0.528736," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{4} b^{2} - {\left(a^{3} b^{3} - a b^{5}\right)} d x - {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} + {\left(a^{5} b + 2 \, a^{3} b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(2 \, a^{5} b + 2 \, a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} - b^{6}\right)} d x\right)} \tan\left(d x + c\right)}{{\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right) + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d}"," ",0,"-(a^4*b^2 - (a^3*b^3 - a*b^5)*d*x - (a^4*b^2 + 2*a^2*b^4 + b^6)*tan(d*x + c)^2 + (a^6 + 2*a^4*b^2 + (a^5*b + 2*a^3*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (a^6 + 2*a^4*b^2 + a^2*b^4 + (a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - (2*a^5*b + 2*a^3*b^3 + a*b^5 + (a^2*b^4 - b^6)*d*x)*tan(d*x + c))/((a^4*b^4 + 2*a^2*b^6 + b^8)*d*tan(d*x + c) + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d)","A",0
470,1,226,0,0.538122," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a^{2} b^{3} d x - 2 \, a^{3} b^{2} - {\left(a^{5} + 3 \, a^{3} b^{2} + {\left(a^{4} b + 3 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(2 \, a b^{4} d x + a^{4} b\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}"," ",0,"-1/2*(4*a^2*b^3*d*x - 2*a^3*b^2 - (a^5 + 3*a^3*b^2 + (a^4*b + 3*a^2*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) + 2*(2*a*b^4*d*x + a^4*b)*tan(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d*tan(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d)","A",0
471,1,153,0,0.456496," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} b + {\left(a^{3} - a b^{2}\right)} d x + {\left(a b^{2} \tan\left(d x + c\right) + a^{2} b\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(a^{3} - {\left(a^{2} b - b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d}"," ",0,"-(a^2*b + (a^3 - a*b^2)*d*x + (a*b^2*tan(d*x + c) + a^2*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (a^3 - (a^2*b - b^3)*d*x)*tan(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d*tan(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d)","A",0
472,1,157,0,0.482591," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} b d x + 2 \, a b^{2} - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(2 \, a b^{2} d x - a^{2} b\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}"," ",0,"1/2*(4*a^2*b*d*x + 2*a*b^2 - (a^3 - a*b^2 + (a^2*b - b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 2*(2*a*b^2*d*x - a^2*b)*tan(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d*tan(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d)","A",0
473,1,154,0,0.437249," ","integrate(1/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b^{3} - {\left(a^{3} - a b^{2}\right)} d x - {\left(a b^{2} \tan\left(d x + c\right) + a^{2} b\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(a b^{2} + {\left(a^{2} b - b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d}"," ",0,"-(b^3 - (a^3 - a*b^2)*d*x - (a*b^2*tan(d*x + c) + a^2*b)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (a*b^2 + (a^2*b - b^3)*d*x)*tan(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d*tan(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d)","A",0
474,1,235,0,0.604250," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a^{4} b d x - 2 \, a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(3 \, a^{3} b^{2} + a b^{4} + {\left(3 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(2 \, a^{3} b^{2} d x + a^{2} b^{3}\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \tan\left(d x + c\right) + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)}}"," ",0,"-1/2*(4*a^4*b*d*x - 2*a*b^4 - (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + (3*a^3*b^2 + a*b^4 + (3*a^2*b^3 + b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 2*(2*a^3*b^2*d*x + a^2*b^3)*tan(d*x + c))/((a^6*b + 2*a^4*b^3 + a^2*b^5)*d*tan(d*x + c) + (a^7 + 2*a^5*b^2 + a^3*b^4)*d)","B",0
475,1,323,0,0.558397," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} - {\left(a^{2} b^{4} - {\left(a^{5} b - a^{3} b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left({\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left({\left(2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(a^{5} b + 2 \, a^{3} b^{3} + 2 \, a b^{5} + {\left(a^{6} - a^{4} b^{2}\right)} d x\right)} \tan\left(d x + c\right)}{{\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \tan\left(d x + c\right)^{2} + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \tan\left(d x + c\right)}"," ",0,"-(a^6 + 2*a^4*b^2 + a^2*b^4 - (a^2*b^4 - (a^5*b - a^3*b^3)*d*x)*tan(d*x + c)^2 + ((a^4*b^2 + 2*a^2*b^4 + b^6)*tan(d*x + c)^2 + (a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - ((2*a^2*b^4 + b^6)*tan(d*x + c)^2 + (2*a^3*b^3 + a*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (a^5*b + 2*a^3*b^3 + 2*a*b^5 + (a^6 - a^4*b^2)*d*x)*tan(d*x + c))/((a^7*b + 2*a^5*b^3 + a^3*b^5)*d*tan(d*x + c)^2 + (a^8 + 2*a^6*b^2 + a^4*b^4)*d*tan(d*x + c))","B",0
476,1,386,0,0.596738," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4} - {\left(4 \, a^{5} b^{2} d x - a^{6} b - 2 \, a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \tan\left(d x + c\right)^{3} - {\left(4 \, a^{6} b d x - a^{7} + 2 \, a^{5} b^{2} + 7 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left({\left(a^{6} b - a^{4} b^{3} - 5 \, a^{2} b^{5} - 3 \, b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \tan\left(d x + c\right)^{2}\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left({\left(5 \, a^{2} b^{5} + 3 \, b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \tan\left(d x + c\right)^{2}\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \tan\left(d x + c\right)^{3} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \tan\left(d x + c\right)^{2}\right)}}"," ",0,"-1/2*(a^7 + 2*a^5*b^2 + a^3*b^4 - (4*a^5*b^2*d*x - a^6*b - 2*a^4*b^3 - 3*a^2*b^5)*tan(d*x + c)^3 - (4*a^6*b*d*x - a^7 + 2*a^5*b^2 + 7*a^3*b^4 + 6*a*b^6)*tan(d*x + c)^2 + ((a^6*b - a^4*b^3 - 5*a^2*b^5 - 3*b^7)*tan(d*x + c)^3 + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*tan(d*x + c)^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) + ((5*a^2*b^5 + 3*b^7)*tan(d*x + c)^3 + (5*a^3*b^4 + 3*a*b^6)*tan(d*x + c)^2)*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(a^6*b + 2*a^4*b^3 + a^2*b^5)*tan(d*x + c))/((a^8*b + 2*a^6*b^3 + a^4*b^5)*d*tan(d*x + c)^3 + (a^9 + 2*a^7*b^2 + a^5*b^4)*d*tan(d*x + c)^2)","B",0
477,1,628,0,0.610234," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 3 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{4} - 4 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{5} - 3 \, a^{3} b^{7}\right)} d x - {\left(18 \, a^{8} b^{2} + 45 \, a^{6} b^{4} + 30 \, a^{4} b^{6} + 8 \, a^{2} b^{8} - b^{10} + 2 \, {\left(a^{3} b^{7} - 3 \, a b^{9}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(6 \, a^{10} + 17 \, a^{8} b^{2} + 15 \, a^{6} b^{4} + {\left(6 \, a^{8} b^{2} + 17 \, a^{6} b^{4} + 15 \, a^{4} b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{9} b + 17 \, a^{7} b^{3} + 15 \, a^{5} b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(6 \, a^{10} + 17 \, a^{8} b^{2} + 15 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - a^{2} b^{8} + {\left(6 \, a^{8} b^{2} + 17 \, a^{6} b^{4} + 15 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{9} b + 17 \, a^{7} b^{3} + 15 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(6 \, a^{9} b + 11 \, a^{7} b^{3} - a b^{9} + 2 \, {\left(a^{4} b^{6} - 3 \, a^{2} b^{8}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{7} + 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} + b^{13}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{6} + 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} + a b^{12}\right)} d \tan\left(d x + c\right) + {\left(a^{8} b^{5} + 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} + a^{2} b^{11}\right)} d\right)}}"," ",0,"1/2*(6*a^8*b^2 + 14*a^6*b^4 + 3*a^4*b^6 + a^2*b^8 + (a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*tan(d*x + c)^4 - 4*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*tan(d*x + c)^3 - 2*(a^5*b^5 - 3*a^3*b^7)*d*x - (18*a^8*b^2 + 45*a^6*b^4 + 30*a^4*b^6 + 8*a^2*b^8 - b^10 + 2*(a^3*b^7 - 3*a*b^9)*d*x)*tan(d*x + c)^2 + (6*a^10 + 17*a^8*b^2 + 15*a^6*b^4 + (6*a^8*b^2 + 17*a^6*b^4 + 15*a^4*b^6)*tan(d*x + c)^2 + 2*(6*a^9*b + 17*a^7*b^3 + 15*a^5*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (6*a^10 + 17*a^8*b^2 + 15*a^6*b^4 + 3*a^4*b^6 - a^2*b^8 + (6*a^8*b^2 + 17*a^6*b^4 + 15*a^4*b^6 + 3*a^2*b^8 - b^10)*tan(d*x + c)^2 + 2*(6*a^9*b + 17*a^7*b^3 + 15*a^5*b^5 + 3*a^3*b^7 - a*b^9)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(6*a^9*b + 11*a^7*b^3 - a*b^9 + 2*(a^4*b^6 - 3*a^2*b^8)*d*x)*tan(d*x + c))/((a^6*b^7 + 3*a^4*b^9 + 3*a^2*b^11 + b^13)*d*tan(d*x + c)^2 + 2*(a^7*b^6 + 3*a^5*b^8 + 3*a^3*b^10 + a*b^12)*d*tan(d*x + c) + (a^8*b^5 + 3*a^6*b^7 + 3*a^4*b^9 + a^2*b^11)*d)","B",0
478,1,549,0,0.608744," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{7} b^{2} + 9 \, a^{5} b^{4} - 2 \, {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d x - {\left(9 \, a^{7} b^{2} + 23 \, a^{5} b^{4} + 12 \, a^{3} b^{6} + 4 \, a b^{8} + 2 \, {\left(3 \, a^{2} b^{7} - b^{9}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, a^{9} + 9 \, a^{7} b^{2} + 10 \, a^{5} b^{4} + {\left(3 \, a^{7} b^{2} + 9 \, a^{5} b^{4} + 10 \, a^{3} b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{8} b + 9 \, a^{6} b^{3} + 10 \, a^{4} b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6} + {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(3 \, a^{8} b + 6 \, a^{6} b^{3} - 2 \, a^{4} b^{5} + a^{2} b^{7} + 2 \, {\left(3 \, a^{3} b^{6} - a b^{8}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} d \tan\left(d x + c\right) + {\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} d\right)}}"," ",0,"-1/2*(3*a^7*b^2 + 9*a^5*b^4 - 2*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*tan(d*x + c)^3 - 2*(3*a^4*b^5 - a^2*b^7)*d*x - (9*a^7*b^2 + 23*a^5*b^4 + 12*a^3*b^6 + 4*a*b^8 + 2*(3*a^2*b^7 - b^9)*d*x)*tan(d*x + c)^2 + (3*a^9 + 9*a^7*b^2 + 10*a^5*b^4 + (3*a^7*b^2 + 9*a^5*b^4 + 10*a^3*b^6)*tan(d*x + c)^2 + 2*(3*a^8*b + 9*a^6*b^3 + 10*a^4*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6 + (a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*tan(d*x + c)^2 + 2*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(3*a^8*b + 6*a^6*b^3 - 2*a^4*b^5 + a^2*b^7 + 2*(3*a^3*b^6 - a*b^8)*d*x)*tan(d*x + c))/((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*d*tan(d*x + c)^2 + 2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*d*tan(d*x + c) + (a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*d)","B",0
479,1,481,0,0.570062," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{6} b^{2} + 7 \, a^{4} b^{4} + 2 \, {\left(a^{5} b^{3} - 3 \, a^{3} b^{5}\right)} d x - {\left(3 \, a^{6} b^{2} + 9 \, a^{4} b^{4} - 2 \, {\left(a^{3} b^{5} - 3 \, a b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 6 \, a^{3} b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} - 4 \, a^{3} b^{5} - 2 \, {\left(a^{4} b^{4} - 3 \, a^{2} b^{6}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right) + {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} d\right)}}"," ",0,"1/2*(a^6*b^2 + 7*a^4*b^4 + 2*(a^5*b^3 - 3*a^3*b^5)*d*x - (3*a^6*b^2 + 9*a^4*b^4 - 2*(a^3*b^5 - 3*a*b^7)*d*x)*tan(d*x + c)^2 + (a^8 + 3*a^6*b^2 + 6*a^4*b^4 + (a^6*b^2 + 3*a^4*b^4 + 6*a^2*b^6)*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 6*a^3*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 2*(a^7*b + 3*a^5*b^3 - 4*a^3*b^5 - 2*(a^4*b^4 - 3*a^2*b^6)*d*x)*tan(d*x + c))/((a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*d*tan(d*x + c)^2 + 2*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*d*tan(d*x + c) + (a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*d)","B",0
480,1,317,0,0.657668," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{5} - 5 \, a^{3} b^{2} - 2 \, {\left(3 \, a^{4} b - a^{2} b^{3}\right)} d x + {\left(a^{5} + 7 \, a^{3} b^{2} - 2 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(a^{5} - 3 \, a^{3} b^{2} + {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 2 \, {\left(3 \, a^{4} b - 3 \, a^{2} b^{3} - 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"1/2*(a^5 - 5*a^3*b^2 - 2*(3*a^4*b - a^2*b^3)*d*x + (a^5 + 7*a^3*b^2 - 2*(3*a^2*b^3 - b^5)*d*x)*tan(d*x + c)^2 + (a^5 - 3*a^3*b^2 + (a^3*b^2 - 3*a*b^4)*tan(d*x + c)^2 + 2*(a^4*b - 3*a^2*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 2*(3*a^4*b - 3*a^2*b^3 - 2*(3*a^3*b^2 - a*b^4)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
481,1,326,0,0.598245," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{4} b - 3 \, a^{2} b^{3} + 2 \, {\left(a^{5} - 3 \, a^{3} b^{2}\right)} d x - {\left(a^{4} b - 5 \, a^{2} b^{3} - 2 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - a^{2} b^{3} + {\left(3 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4} - 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"-1/2*(3*a^4*b - 3*a^2*b^3 + 2*(a^5 - 3*a^3*b^2)*d*x - (a^4*b - 5*a^2*b^3 - 2*(a^3*b^2 - 3*a*b^4)*d*x)*tan(d*x + c)^2 + (3*a^4*b - a^2*b^3 + (3*a^2*b^3 - b^5)*tan(d*x + c)^2 + 2*(3*a^3*b^2 - a*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(a^5 - 3*a^3*b^2 + 2*a*b^4 - 2*(a^4*b - 3*a^2*b^3)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
482,1,328,0,0.860416," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{5 \, a^{3} b^{2} - a b^{4} + 2 \, {\left(3 \, a^{4} b - a^{2} b^{3}\right)} d x - {\left(3 \, a^{3} b^{2} - 3 \, a b^{4} - 2 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left(a^{5} - 3 \, a^{3} b^{2} + {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5} - 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"1/2*(5*a^3*b^2 - a*b^4 + 2*(3*a^4*b - a^2*b^3)*d*x - (3*a^3*b^2 - 3*a*b^4 - 2*(3*a^2*b^3 - b^5)*d*x)*tan(d*x + c)^2 - (a^5 - 3*a^3*b^2 + (a^3*b^2 - 3*a*b^4)*tan(d*x + c)^2 + 2*(a^4*b - 3*a^2*b^3)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(2*a^4*b - 3*a^2*b^3 + b^5 - 2*(3*a^3*b^2 - a*b^4)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
483,1,321,0,0.616855," ","integrate(1/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{7 \, a^{2} b^{3} + b^{5} - 2 \, {\left(a^{5} - 3 \, a^{3} b^{2}\right)} d x - {\left(5 \, a^{2} b^{3} - b^{5} + 2 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{2} - {\left(3 \, a^{4} b - a^{2} b^{3} + {\left(3 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(3 \, a^{3} b^{2} - 3 \, a b^{4} + 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d\right)}}"," ",0,"-1/2*(7*a^2*b^3 + b^5 - 2*(a^5 - 3*a^3*b^2)*d*x - (5*a^2*b^3 - b^5 + 2*(a^3*b^2 - 3*a*b^4)*d*x)*tan(d*x + c)^2 - (3*a^4*b - a^2*b^3 + (3*a^2*b^3 - b^5)*tan(d*x + c)^2 + 2*(3*a^3*b^2 - a*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(3*a^3*b^2 - 3*a*b^4 + 2*(a^4*b - 3*a^2*b^3)*d*x)*tan(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*tan(d*x + c) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d)","B",0
484,1,494,0,0.604079," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{9 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - 2 \, {\left(3 \, a^{7} b - a^{5} b^{3}\right)} d x - {\left(7 \, a^{4} b^{4} + a^{2} b^{6} + 2 \, {\left(3 \, a^{5} b^{3} - a^{3} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6} + {\left(6 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 2 \, {\left(4 \, a^{5} b^{3} - 3 \, a^{3} b^{5} - a b^{7} + 2 \, {\left(3 \, a^{6} b^{2} - a^{4} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} + a^{5} b^{6}\right)} d\right)}}"," ",0,"1/2*(9*a^4*b^4 + 3*a^2*b^6 - 2*(3*a^7*b - a^5*b^3)*d*x - (7*a^4*b^4 + a^2*b^6 + 2*(3*a^5*b^3 - a^3*b^5)*d*x)*tan(d*x + c)^2 + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - (6*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 + (6*a^4*b^4 + 3*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(6*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 2*(4*a^5*b^3 - 3*a^3*b^5 - a*b^7 + 2*(3*a^6*b^2 - a^4*b^4)*d*x)*tan(d*x + c))/((a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*d*tan(d*x + c)^2 + 2*(a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7)*d*tan(d*x + c) + (a^11 + 3*a^9*b^2 + 3*a^7*b^4 + a^5*b^6)*d)","B",0
485,1,585,0,0.524936," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{9} + 6 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 2 \, a^{3} b^{6} - {\left(9 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + 6 \, a^{3} b^{6} + 3 \, a b^{8} + 2 \, {\left(a^{8} b - 3 \, a^{6} b^{3}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - {\left({\left(10 \, a^{4} b^{5} + 9 \, a^{2} b^{7} + 3 \, b^{9}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(10 \, a^{5} b^{4} + 9 \, a^{3} b^{6} + 3 \, a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(10 \, a^{6} b^{3} + 9 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(4 \, a^{8} b + 12 \, a^{6} b^{3} + 23 \, a^{4} b^{5} + 9 \, a^{2} b^{7} + 2 \, {\left(a^{9} - 3 \, a^{7} b^{2}\right)} d x\right)} \tan\left(d x + c\right)}{2 \, {\left({\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} d \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} d \tan\left(d x + c\right)^{2} + {\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} d \tan\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^9 + 6*a^7*b^2 + 6*a^5*b^4 + 2*a^3*b^6 - (9*a^4*b^5 + 3*a^2*b^7 - 2*(a^7*b^2 - 3*a^5*b^4)*d*x)*tan(d*x + c)^3 + 2*(a^7*b^2 - 2*a^5*b^4 + 6*a^3*b^6 + 3*a*b^8 + 2*(a^8*b - 3*a^6*b^3)*d*x)*tan(d*x + c)^2 + 3*((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*tan(d*x + c)^3 + 2*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*tan(d*x + c)^2 + (a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - ((10*a^4*b^5 + 9*a^2*b^7 + 3*b^9)*tan(d*x + c)^3 + 2*(10*a^5*b^4 + 9*a^3*b^6 + 3*a*b^8)*tan(d*x + c)^2 + (10*a^6*b^3 + 9*a^4*b^5 + 3*a^2*b^7)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (4*a^8*b + 12*a^6*b^3 + 23*a^4*b^5 + 9*a^2*b^7 + 2*(a^9 - 3*a^7*b^2)*d*x)*tan(d*x + c))/((a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*d*tan(d*x + c)^3 + 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*d*tan(d*x + c)^2 + (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*d*tan(d*x + c))","B",0
486,1,886,0,0.619669," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, a^{10} b^{2} + 21 \, a^{8} b^{4} + 37 \, a^{6} b^{6} - 3 \, {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{4} - {\left(22 \, a^{9} b^{3} + 81 \, a^{7} b^{5} + 108 \, a^{5} b^{7} + 36 \, a^{3} b^{9} + 9 \, a b^{11} - 3 \, {\left(a^{4} b^{8} - 6 \, a^{2} b^{10} + b^{12}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{5} - 6 \, a^{5} b^{7} + a^{3} b^{9}\right)} d x - 3 \, {\left(10 \, a^{10} b^{2} + 34 \, a^{8} b^{4} + 40 \, a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - 3 \, {\left(a^{5} b^{7} - 6 \, a^{3} b^{9} + a b^{11}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 5 \, a^{6} b^{6} + {\left(a^{9} b^{3} + 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 5 \, a^{4} b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 5 \, a^{5} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 6 \, {\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8} + {\left(a^{9} b^{3} + 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 4 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(4 \, a^{11} b + 10 \, a^{9} b^{3} + 4 \, a^{7} b^{5} - 23 \, a^{5} b^{7} + a^{3} b^{9} - 3 \, {\left(a^{6} b^{6} - 6 \, a^{4} b^{8} + a^{2} b^{10}\right)} d x\right)} \tan\left(d x + c\right)}{3 \, {\left({\left(a^{8} b^{8} + 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} + 4 \, a^{2} b^{14} + b^{16}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} + 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} + 4 \, a^{3} b^{13} + a b^{15}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{6} + 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} + 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \tan\left(d x + c\right) + {\left(a^{11} b^{5} + 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} + 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d\right)}}"," ",0,"-1/3*(6*a^10*b^2 + 21*a^8*b^4 + 37*a^6*b^6 - 3*(a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*tan(d*x + c)^4 - (22*a^9*b^3 + 81*a^7*b^5 + 108*a^5*b^7 + 36*a^3*b^9 + 9*a*b^11 - 3*(a^4*b^8 - 6*a^2*b^10 + b^12)*d*x)*tan(d*x + c)^3 + 3*(a^7*b^5 - 6*a^5*b^7 + a^3*b^9)*d*x - 3*(10*a^10*b^2 + 34*a^8*b^4 + 40*a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - 3*(a^5*b^7 - 6*a^3*b^9 + a*b^11)*d*x)*tan(d*x + c)^2 + 6*(a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 5*a^6*b^6 + (a^9*b^3 + 4*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9)*tan(d*x + c)^3 + 3*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 5*a^4*b^8)*tan(d*x + c)^2 + 3*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 5*a^5*b^7)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 6*(a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8 + (a^9*b^3 + 4*a^7*b^5 + 6*a^5*b^7 + 4*a^3*b^9 + a*b^11)*tan(d*x + c)^3 + 3*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*tan(d*x + c)^2 + 3*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 3*(4*a^11*b + 10*a^9*b^3 + 4*a^7*b^5 - 23*a^5*b^7 + a^3*b^9 - 3*(a^6*b^6 - 6*a^4*b^8 + a^2*b^10)*d*x)*tan(d*x + c))/((a^8*b^8 + 4*a^6*b^10 + 6*a^4*b^12 + 4*a^2*b^14 + b^16)*d*tan(d*x + c)^3 + 3*(a^9*b^7 + 4*a^7*b^9 + 6*a^5*b^11 + 4*a^3*b^13 + a*b^15)*d*tan(d*x + c)^2 + 3*(a^10*b^6 + 4*a^8*b^8 + 6*a^6*b^10 + 4*a^4*b^12 + a^2*b^14)*d*tan(d*x + c) + (a^11*b^5 + 4*a^9*b^7 + 6*a^7*b^9 + 4*a^5*b^11 + a^3*b^13)*d)","B",0
487,1,784,0,0.617415," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 47 \, a^{5} b^{6} - {\left(11 \, a^{8} b^{3} + 42 \, a^{6} b^{5} + 75 \, a^{4} b^{7} - 24 \, {\left(a^{3} b^{8} - a b^{10}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 24 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} d x - 3 \, {\left(5 \, a^{9} b^{2} + 18 \, a^{7} b^{4} + 37 \, a^{5} b^{6} - 20 \, a^{3} b^{8} - 24 \, {\left(a^{4} b^{7} - a^{2} b^{9}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{11} + 4 \, a^{9} b^{2} + 5 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 5 \, a^{4} b^{7} + 10 \, a^{2} b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 5 \, a^{5} b^{6} + 10 \, a^{3} b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 5 \, a^{6} b^{5} + 10 \, a^{4} b^{7}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(2 \, a^{10} b + 5 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 35 \, a^{4} b^{7} - 24 \, {\left(a^{5} b^{6} - a^{3} b^{8}\right)} d x\right)} \tan\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{7} + 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + 4 \, a^{2} b^{13} + b^{15}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{6} + 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} + 4 \, a^{3} b^{12} + a b^{14}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{5} + 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} + 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \tan\left(d x + c\right) + {\left(a^{11} b^{4} + 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} + 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d\right)}}"," ",0,"1/6*(3*a^9*b^2 + 6*a^7*b^4 + 47*a^5*b^6 - (11*a^8*b^3 + 42*a^6*b^5 + 75*a^4*b^7 - 24*(a^3*b^8 - a*b^10)*d*x)*tan(d*x + c)^3 + 24*(a^6*b^5 - a^4*b^7)*d*x - 3*(5*a^9*b^2 + 18*a^7*b^4 + 37*a^5*b^6 - 20*a^3*b^8 - 24*(a^4*b^7 - a^2*b^9)*d*x)*tan(d*x + c)^2 + 3*(a^11 + 4*a^9*b^2 + 5*a^7*b^4 + 10*a^5*b^6 + (a^8*b^3 + 4*a^6*b^5 + 5*a^4*b^7 + 10*a^2*b^9)*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 5*a^5*b^6 + 10*a^3*b^8)*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 5*a^6*b^5 + 10*a^4*b^7)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*tan(d*x + c))*log(1/(tan(d*x + c)^2 + 1)) - 3*(2*a^10*b + 5*a^8*b^3 + 12*a^6*b^5 - 35*a^4*b^7 - 24*(a^5*b^6 - a^3*b^8)*d*x)*tan(d*x + c))/((a^8*b^7 + 4*a^6*b^9 + 6*a^4*b^11 + 4*a^2*b^13 + b^15)*d*tan(d*x + c)^3 + 3*(a^9*b^6 + 4*a^7*b^8 + 6*a^5*b^10 + 4*a^3*b^12 + a*b^14)*d*tan(d*x + c)^2 + 3*(a^10*b^5 + 4*a^8*b^7 + 6*a^6*b^9 + 4*a^4*b^11 + a^2*b^13)*d*tan(d*x + c) + (a^11*b^4 + 4*a^9*b^6 + 6*a^7*b^8 + 4*a^5*b^10 + a^3*b^12)*d)","B",0
488,1,510,0,0.516446," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{9 \, a^{6} b - 13 \, a^{4} b^{3} + {\left(a^{7} + 3 \, a^{5} b^{2} + 24 \, a^{3} b^{4} + 3 \, {\left(a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} - 6 \, a^{5} b^{2} + a^{3} b^{4}\right)} d x - 3 \, {\left(a^{6} b - 15 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 3 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(a^{6} b - a^{4} b^{3} + {\left(a^{3} b^{4} - a b^{6}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(a^{7} - 11 \, a^{5} b^{2} + 10 \, a^{3} b^{4} - 3 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x\right)} \tan\left(d x + c\right)}{3 \, {\left({\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}"," ",0,"1/3*(9*a^6*b - 13*a^4*b^3 + (a^7 + 3*a^5*b^2 + 24*a^3*b^4 + 3*(a^4*b^3 - 6*a^2*b^5 + b^7)*d*x)*tan(d*x + c)^3 + 3*(a^7 - 6*a^5*b^2 + a^3*b^4)*d*x - 3*(a^6*b - 15*a^4*b^3 + 6*a^2*b^5 - 3*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*d*x)*tan(d*x + c)^2 + 6*(a^6*b - a^4*b^3 + (a^3*b^4 - a*b^6)*tan(d*x + c)^3 + 3*(a^4*b^3 - a^2*b^5)*tan(d*x + c)^2 + 3*(a^5*b^2 - a^3*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(a^7 - 11*a^5*b^2 + 10*a^3*b^4 - 3*(a^6*b - 6*a^4*b^3 + a^2*b^5)*d*x)*tan(d*x + c))/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*d*tan(d*x + c) + (a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8)*d)","B",0
489,1,526,0,0.508203," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{7} - 30 \, a^{5} b^{2} + 11 \, a^{3} b^{4} + {\left(a^{6} b + 18 \, a^{4} b^{3} - 27 \, a^{2} b^{5} - 24 \, {\left(a^{3} b^{4} - a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 24 \, {\left(a^{6} b - a^{4} b^{3}\right)} d x + 3 \, {\left(a^{7} + 16 \, a^{5} b^{2} - 23 \, a^{3} b^{4} + 6 \, a b^{6} - 24 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{7} - 6 \, a^{5} b^{2} + a^{3} b^{4} + {\left(a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + a^{2} b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + 3 \, {\left(9 \, a^{6} b - 26 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - 24 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}"," ",0,"1/6*(3*a^7 - 30*a^5*b^2 + 11*a^3*b^4 + (a^6*b + 18*a^4*b^3 - 27*a^2*b^5 - 24*(a^3*b^4 - a*b^6)*d*x)*tan(d*x + c)^3 - 24*(a^6*b - a^4*b^3)*d*x + 3*(a^7 + 16*a^5*b^2 - 23*a^3*b^4 + 6*a*b^6 - 24*(a^4*b^3 - a^2*b^5)*d*x)*tan(d*x + c)^2 + 3*(a^7 - 6*a^5*b^2 + a^3*b^4 + (a^4*b^3 - 6*a^2*b^5 + b^7)*tan(d*x + c)^3 + 3*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*tan(d*x + c)^2 + 3*(a^6*b - 6*a^4*b^3 + a^2*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + 3*(9*a^6*b - 26*a^4*b^3 + 9*a^2*b^5 - 24*(a^5*b^2 - a^3*b^4)*d*x)*tan(d*x + c))/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*d*tan(d*x + c) + (a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8)*d)","B",0
490,1,531,0,0.517739," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, a^{6} b - 15 \, a^{4} b^{3} + a^{2} b^{5} - {\left(a^{5} b^{2} - 15 \, a^{3} b^{4} + 6 \, a b^{6} - 3 \, {\left(a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} - 6 \, a^{5} b^{2} + a^{3} b^{4}\right)} d x - 3 \, {\left(a^{6} b - 12 \, a^{4} b^{3} + 8 \, a^{2} b^{5} - b^{7} - 3 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(a^{6} b - a^{4} b^{3} + {\left(a^{3} b^{4} - a b^{6}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(a^{7} - 8 \, a^{5} b^{2} + 12 \, a^{3} b^{4} - a b^{6} - 3 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x\right)} \tan\left(d x + c\right)}{3 \, {\left({\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}"," ",0,"-1/3*(6*a^6*b - 15*a^4*b^3 + a^2*b^5 - (a^5*b^2 - 15*a^3*b^4 + 6*a*b^6 - 3*(a^4*b^3 - 6*a^2*b^5 + b^7)*d*x)*tan(d*x + c)^3 + 3*(a^7 - 6*a^5*b^2 + a^3*b^4)*d*x - 3*(a^6*b - 12*a^4*b^3 + 8*a^2*b^5 - b^7 - 3*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*d*x)*tan(d*x + c)^2 + 6*(a^6*b - a^4*b^3 + (a^3*b^4 - a*b^6)*tan(d*x + c)^3 + 3*(a^4*b^3 - a^2*b^5)*tan(d*x + c)^2 + 3*(a^5*b^2 - a^3*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(a^7 - 8*a^5*b^2 + 12*a^3*b^4 - a*b^6 - 3*(a^6*b - 6*a^4*b^3 + a^2*b^5)*d*x)*tan(d*x + c))/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*d*tan(d*x + c) + (a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8)*d)","B",0
491,1,528,0,0.513967," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{27 \, a^{5} b^{2} - 18 \, a^{3} b^{4} - a b^{6} - {\left(11 \, a^{4} b^{3} - 30 \, a^{2} b^{5} + 3 \, b^{7} - 24 \, {\left(a^{3} b^{4} - a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 24 \, {\left(a^{6} b - a^{4} b^{3}\right)} d x - 3 \, {\left(9 \, a^{5} b^{2} - 26 \, a^{3} b^{4} + 9 \, a b^{6} - 24 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(a^{7} - 6 \, a^{5} b^{2} + a^{3} b^{4} + {\left(a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + a^{2} b^{5}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(6 \, a^{6} b - 23 \, a^{4} b^{3} + 16 \, a^{2} b^{5} + b^{7} - 24 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}"," ",0,"1/6*(27*a^5*b^2 - 18*a^3*b^4 - a*b^6 - (11*a^4*b^3 - 30*a^2*b^5 + 3*b^7 - 24*(a^3*b^4 - a*b^6)*d*x)*tan(d*x + c)^3 + 24*(a^6*b - a^4*b^3)*d*x - 3*(9*a^5*b^2 - 26*a^3*b^4 + 9*a*b^6 - 24*(a^4*b^3 - a^2*b^5)*d*x)*tan(d*x + c)^2 - 3*(a^7 - 6*a^5*b^2 + a^3*b^4 + (a^4*b^3 - 6*a^2*b^5 + b^7)*tan(d*x + c)^3 + 3*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*tan(d*x + c)^2 + 3*(a^6*b - 6*a^4*b^3 + a^2*b^5)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(6*a^6*b - 23*a^4*b^3 + 16*a^2*b^5 + b^7 - 24*(a^5*b^2 - a^3*b^4)*d*x)*tan(d*x + c))/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*d*tan(d*x + c) + (a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8)*d)","B",0
492,1,511,0,0.491595," ","integrate(1/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{24 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7} - {\left(13 \, a^{3} b^{4} - 9 \, a b^{6} + 3 \, {\left(a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 3 \, {\left(a^{7} - 6 \, a^{5} b^{2} + a^{3} b^{4}\right)} d x - 3 \, {\left(10 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + b^{7} + 3 \, {\left(a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(a^{6} b - a^{4} b^{3} + {\left(a^{3} b^{4} - a b^{6}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(6 \, a^{5} b^{2} - 15 \, a^{3} b^{4} + a b^{6} + 3 \, {\left(a^{6} b - 6 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x\right)} \tan\left(d x + c\right)}{3 \, {\left({\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}"," ",0,"-1/3*(24*a^4*b^3 + 3*a^2*b^5 + b^7 - (13*a^3*b^4 - 9*a*b^6 + 3*(a^4*b^3 - 6*a^2*b^5 + b^7)*d*x)*tan(d*x + c)^3 - 3*(a^7 - 6*a^5*b^2 + a^3*b^4)*d*x - 3*(10*a^4*b^3 - 11*a^2*b^5 + b^7 + 3*(a^5*b^2 - 6*a^3*b^4 + a*b^6)*d*x)*tan(d*x + c)^2 - 6*(a^6*b - a^4*b^3 + (a^3*b^4 - a*b^6)*tan(d*x + c)^3 + 3*(a^4*b^3 - a^2*b^5)*tan(d*x + c)^2 + 3*(a^5*b^2 - a^3*b^4)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(6*a^5*b^2 - 15*a^3*b^4 + a*b^6 + 3*(a^6*b - 6*a^4*b^3 + a^2*b^5)*d*x)*tan(d*x + c))/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*d*tan(d*x + c) + (a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8)*d)","B",0
493,1,793,0,0.702490," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{75 \, a^{7} b^{4} + 42 \, a^{5} b^{6} + 11 \, a^{3} b^{8} - {\left(47 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + 24 \, {\left(a^{7} b^{4} - a^{5} b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{3} - 24 \, {\left(a^{10} b - a^{8} b^{3}\right)} d x - 3 \, {\left(35 \, a^{7} b^{4} - 12 \, a^{5} b^{6} - 5 \, a^{3} b^{8} - 2 \, a b^{10} + 24 \, {\left(a^{8} b^{3} - a^{6} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(10 \, a^{9} b^{2} + 5 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(10 \, a^{6} b^{5} + 5 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(10 \, a^{7} b^{4} + 5 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(10 \, a^{8} b^{3} + 5 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, {\left(20 \, a^{8} b^{3} - 37 \, a^{6} b^{5} - 18 \, a^{4} b^{7} - 5 \, a^{2} b^{9} + 24 \, {\left(a^{9} b^{2} - a^{7} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{6 \, {\left({\left(a^{12} b^{3} + 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} + 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{13} b^{2} + 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} + 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b + 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} + 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \tan\left(d x + c\right) + {\left(a^{15} + 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} + 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d\right)}}"," ",0,"1/6*(75*a^7*b^4 + 42*a^5*b^6 + 11*a^3*b^8 - (47*a^6*b^5 + 6*a^4*b^7 + 3*a^2*b^9 + 24*(a^7*b^4 - a^5*b^6)*d*x)*tan(d*x + c)^3 - 24*(a^10*b - a^8*b^3)*d*x - 3*(35*a^7*b^4 - 12*a^5*b^6 - 5*a^3*b^8 - 2*a*b^10 + 24*(a^8*b^3 - a^6*b^5)*d*x)*tan(d*x + c)^2 + 3*(a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*tan(d*x + c)^3 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - 3*(10*a^9*b^2 + 5*a^7*b^4 + 4*a^5*b^6 + a^3*b^8 + (10*a^6*b^5 + 5*a^4*b^7 + 4*a^2*b^9 + b^11)*tan(d*x + c)^3 + 3*(10*a^7*b^4 + 5*a^5*b^6 + 4*a^3*b^8 + a*b^10)*tan(d*x + c)^2 + 3*(10*a^8*b^3 + 5*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) - 3*(20*a^8*b^3 - 37*a^6*b^5 - 18*a^4*b^7 - 5*a^2*b^9 + 24*(a^9*b^2 - a^7*b^4)*d*x)*tan(d*x + c))/((a^12*b^3 + 4*a^10*b^5 + 6*a^8*b^7 + 4*a^6*b^9 + a^4*b^11)*d*tan(d*x + c)^3 + 3*(a^13*b^2 + 4*a^11*b^4 + 6*a^9*b^6 + 4*a^7*b^8 + a^5*b^10)*d*tan(d*x + c)^2 + 3*(a^14*b + 4*a^12*b^3 + 6*a^10*b^5 + 4*a^8*b^7 + a^6*b^9)*d*tan(d*x + c) + (a^15 + 4*a^13*b^2 + 6*a^11*b^4 + 4*a^9*b^6 + a^7*b^8)*d)","B",0
494,1,925,0,0.675956," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, a^{12} + 12 \, a^{10} b^{2} + 18 \, a^{8} b^{4} + 12 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - {\left(37 \, a^{6} b^{6} + 21 \, a^{4} b^{8} + 6 \, a^{2} b^{10} - 3 \, {\left(a^{9} b^{3} - 6 \, a^{7} b^{5} + a^{5} b^{7}\right)} d x\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{9} b^{3} - 23 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + 10 \, a^{3} b^{9} + 4 \, a b^{11} + 3 \, {\left(a^{10} b^{2} - 6 \, a^{8} b^{4} + a^{6} b^{6}\right)} d x\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{10} b^{2} - 3 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 34 \, a^{4} b^{8} + 10 \, a^{2} b^{10} + 3 \, {\left(a^{11} b - 6 \, a^{9} b^{3} + a^{7} b^{5}\right)} d x\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{9} b^{3} + 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 4 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) - 6 \, {\left({\left(5 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 4 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \tan\left(d x + c\right)^{2} + {\left(5 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \tan\left(d x + c\right)\right)} \log\left(\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) + {\left(9 \, a^{11} b + 36 \, a^{9} b^{3} + 108 \, a^{7} b^{5} + 81 \, a^{5} b^{7} + 22 \, a^{3} b^{9} + 3 \, {\left(a^{12} - 6 \, a^{10} b^{2} + a^{8} b^{4}\right)} d x\right)} \tan\left(d x + c\right)}{3 \, {\left({\left(a^{13} b^{3} + 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} + 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{14} b^{2} + 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} + 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b + 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} + 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \tan\left(d x + c\right)^{2} + {\left(a^{16} + 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} + 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \tan\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*a^12 + 12*a^10*b^2 + 18*a^8*b^4 + 12*a^6*b^6 + 3*a^4*b^8 - (37*a^6*b^6 + 21*a^4*b^8 + 6*a^2*b^10 - 3*(a^9*b^3 - 6*a^7*b^5 + a^5*b^7)*d*x)*tan(d*x + c)^4 + 3*(a^9*b^3 - 23*a^7*b^5 + 4*a^5*b^7 + 10*a^3*b^9 + 4*a*b^11 + 3*(a^10*b^2 - 6*a^8*b^4 + a^6*b^6)*d*x)*tan(d*x + c)^3 + 3*(3*a^10*b^2 - 3*a^8*b^4 + 40*a^6*b^6 + 34*a^4*b^8 + 10*a^2*b^10 + 3*(a^11*b - 6*a^9*b^3 + a^7*b^5)*d*x)*tan(d*x + c)^2 + 6*((a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*tan(d*x + c)^4 + 3*(a^9*b^3 + 4*a^7*b^5 + 6*a^5*b^7 + 4*a^3*b^9 + a*b^11)*tan(d*x + c)^3 + 3*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*tan(d*x + c)^2 + (a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*tan(d*x + c))*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1)) - 6*((5*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*tan(d*x + c)^4 + 3*(5*a^7*b^5 + 6*a^5*b^7 + 4*a^3*b^9 + a*b^11)*tan(d*x + c)^3 + 3*(5*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*tan(d*x + c)^2 + (5*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*tan(d*x + c))*log((b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2)/(tan(d*x + c)^2 + 1)) + (9*a^11*b + 36*a^9*b^3 + 108*a^7*b^5 + 81*a^5*b^7 + 22*a^3*b^9 + 3*(a^12 - 6*a^10*b^2 + a^8*b^4)*d*x)*tan(d*x + c))/((a^13*b^3 + 4*a^11*b^5 + 6*a^9*b^7 + 4*a^7*b^9 + a^5*b^11)*d*tan(d*x + c)^4 + 3*(a^14*b^2 + 4*a^12*b^4 + 6*a^10*b^6 + 4*a^8*b^8 + a^6*b^10)*d*tan(d*x + c)^3 + 3*(a^15*b + 4*a^13*b^3 + 6*a^11*b^5 + 4*a^9*b^7 + a^7*b^9)*d*tan(d*x + c)^2 + (a^16 + 4*a^14*b^2 + 6*a^12*b^4 + 4*a^10*b^6 + a^8*b^8)*d*tan(d*x + c))","B",0
495,1,46,0,0.465026," ","integrate(1/(3+5*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, d x + 5 \, \log\left(\frac{25 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 9}{\tan\left(d x + c\right)^{2} + 1}\right)}{68 \, d}"," ",0,"1/68*(6*d*x + 5*log((25*tan(d*x + c)^2 + 30*tan(d*x + c) + 9)/(tan(d*x + c)^2 + 1)))/d","A",0
496,1,83,0,0.462948," ","integrate(1/(3+5*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, d x - 15 \, {\left(5 \, \tan\left(d x + c\right) + 3\right)} \log\left(\frac{25 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 9}{\tan\left(d x + c\right)^{2} + 1}\right) + 5 \, {\left(16 \, d x - 15\right)} \tan\left(d x + c\right) + 125}{1156 \, {\left(5 \, d \tan\left(d x + c\right) + 3 \, d\right)}}"," ",0,"-1/1156*(48*d*x - 15*(5*tan(d*x + c) + 3)*log((25*tan(d*x + c)^2 + 30*tan(d*x + c) + 9)/(tan(d*x + c)^2 + 1)) + 5*(16*d*x - 15)*tan(d*x + c) + 125)/(5*d*tan(d*x + c) + 3*d)","A",0
497,1,120,0,0.483195," ","integrate(1/(3+5*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{50 \, {\left(99 \, d x - 25\right)} \tan\left(d x + c\right)^{2} + 1782 \, d x - 5 \, {\left(25 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 9\right)} \log\left(\frac{25 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 9}{\tan\left(d x + c\right)^{2} + 1}\right) + 180 \, {\left(33 \, d x + 20\right)} \tan\left(d x + c\right) + 5500}{39304 \, {\left(25 \, d \tan\left(d x + c\right)^{2} + 30 \, d \tan\left(d x + c\right) + 9 \, d\right)}}"," ",0,"-1/39304*(50*(99*d*x - 25)*tan(d*x + c)^2 + 1782*d*x - 5*(25*tan(d*x + c)^2 + 30*tan(d*x + c) + 9)*log((25*tan(d*x + c)^2 + 30*tan(d*x + c) + 9)/(tan(d*x + c)^2 + 1)) + 180*(33*d*x + 20)*tan(d*x + c) + 5500)/(25*d*tan(d*x + c)^2 + 30*d*tan(d*x + c) + 9*d)","A",0
498,1,157,0,0.445995," ","integrate(1/(3+5*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{375 \, {\left(161 \, d x + 135\right)} \tan\left(d x + c\right)^{3} + 75 \, {\left(1449 \, d x + 1300\right)} \tan\left(d x + c\right)^{2} + 13041 \, d x + 360 \, {\left(125 \, \tan\left(d x + c\right)^{3} + 225 \, \tan\left(d x + c\right)^{2} + 135 \, \tan\left(d x + c\right) + 27\right)} \log\left(\frac{25 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 9}{\tan\left(d x + c\right)^{2} + 1}\right) + 45 \, {\left(1449 \, d x + 2830\right)} \tan\left(d x + c\right) + 101375}{1002252 \, {\left(125 \, d \tan\left(d x + c\right)^{3} + 225 \, d \tan\left(d x + c\right)^{2} + 135 \, d \tan\left(d x + c\right) + 27 \, d\right)}}"," ",0,"-1/1002252*(375*(161*d*x + 135)*tan(d*x + c)^3 + 75*(1449*d*x + 1300)*tan(d*x + c)^2 + 13041*d*x + 360*(125*tan(d*x + c)^3 + 225*tan(d*x + c)^2 + 135*tan(d*x + c) + 27)*log((25*tan(d*x + c)^2 + 30*tan(d*x + c) + 9)/(tan(d*x + c)^2 + 1)) + 45*(1449*d*x + 2830)*tan(d*x + c) + 101375)/(125*d*tan(d*x + c)^3 + 225*d*tan(d*x + c)^2 + 135*d*tan(d*x + c) + 27*d)","B",0
499,1,46,0,0.467010," ","integrate(1/(5+3*tan(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, d x + 3 \, \log\left(\frac{9 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 25}{\tan\left(d x + c\right)^{2} + 1}\right)}{68 \, d}"," ",0,"1/68*(10*d*x + 3*log((9*tan(d*x + c)^2 + 30*tan(d*x + c) + 25)/(tan(d*x + c)^2 + 1)))/d","A",0
500,1,83,0,0.510417," ","integrate(1/(5+3*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{80 \, d x + 15 \, {\left(3 \, \tan\left(d x + c\right) + 5\right)} \log\left(\frac{9 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 25}{\tan\left(d x + c\right)^{2} + 1}\right) + 3 \, {\left(16 \, d x + 15\right)} \tan\left(d x + c\right) - 27}{1156 \, {\left(3 \, d \tan\left(d x + c\right) + 5 \, d\right)}}"," ",0,"1/1156*(80*d*x + 15*(3*tan(d*x + c) + 5)*log((9*tan(d*x + c)^2 + 30*tan(d*x + c) + 25)/(tan(d*x + c)^2 + 1)) + 3*(16*d*x + 15)*tan(d*x + c) - 27)/(3*d*tan(d*x + c) + 5*d)","A",0
501,1,120,0,0.472902," ","integrate(1/(5+3*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{18 \, {\left(5 \, d x - 87\right)} \tan\left(d x + c\right)^{2} + 250 \, d x - 99 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 25\right)} \log\left(\frac{9 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 25}{\tan\left(d x + c\right)^{2} + 1}\right) + 60 \, {\left(5 \, d x - 36\right)} \tan\left(d x + c\right) + 2484}{39304 \, {\left(9 \, d \tan\left(d x + c\right)^{2} + 30 \, d \tan\left(d x + c\right) + 25 \, d\right)}}"," ",0,"-1/39304*(18*(5*d*x - 87)*tan(d*x + c)^2 + 250*d*x - 99*(9*tan(d*x + c)^2 + 30*tan(d*x + c) + 25)*log((9*tan(d*x + c)^2 + 30*tan(d*x + c) + 25)/(tan(d*x + c)^2 + 1)) + 60*(5*d*x - 36)*tan(d*x + c) + 2484)/(9*d*tan(d*x + c)^2 + 30*d*tan(d*x + c) + 25*d)","A",0
502,1,157,0,0.455897," ","integrate(1/(5+3*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{27 \, {\left(161 \, d x - 305\right)} \tan\left(d x + c\right)^{3} + 27 \, {\left(805 \, d x - 964\right)} \tan\left(d x + c\right)^{2} + 20125 \, d x - 120 \, {\left(27 \, \tan\left(d x + c\right)^{3} + 135 \, \tan\left(d x + c\right)^{2} + 225 \, \tan\left(d x + c\right) + 125\right)} \log\left(\frac{9 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 25}{\tan\left(d x + c\right)^{2} + 1}\right) + 45 \, {\left(805 \, d x - 114\right)} \tan\left(d x + c\right) + 35451}{334084 \, {\left(27 \, d \tan\left(d x + c\right)^{3} + 135 \, d \tan\left(d x + c\right)^{2} + 225 \, d \tan\left(d x + c\right) + 125 \, d\right)}}"," ",0,"-1/334084*(27*(161*d*x - 305)*tan(d*x + c)^3 + 27*(805*d*x - 964)*tan(d*x + c)^2 + 20125*d*x - 120*(27*tan(d*x + c)^3 + 135*tan(d*x + c)^2 + 225*tan(d*x + c) + 125)*log((9*tan(d*x + c)^2 + 30*tan(d*x + c) + 25)/(tan(d*x + c)^2 + 1)) + 45*(805*d*x - 114)*tan(d*x + c) + 35451)/(27*d*tan(d*x + c)^3 + 135*d*tan(d*x + c)^2 + 225*d*tan(d*x + c) + 125*d)","B",0
503,1,1682,0,0.547897," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""fricas"")","-\frac{420 \, \sqrt{2} b^{3} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} b^{3} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{3} - 105 \, \sqrt{2} {\left(a b^{3} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 105 \, \sqrt{2} {\left(a b^{3} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(2 \, {\left(4 \, a^{5} - 15 \, a^{3} b^{2} - 19 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(15 \, a^{2} b^{3} + 15 \, b^{5} - 2 \, {\left(2 \, a^{4} b + 27 \, a^{2} b^{3} + 25 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{420 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"-1/420*(420*sqrt(2)*b^3*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) + (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4))*cos(d*x + c)^3 + 420*sqrt(2)*b^3*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) - (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4))*cos(d*x + c)^3 - 105*sqrt(2)*(a*b^3*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c)^3 - (a^2*b^3 + b^5)*d*cos(d*x + c)^3)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 105*sqrt(2)*(a*b^3*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c)^3 - (a^2*b^3 + b^5)*d*cos(d*x + c)^3)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(2*(4*a^5 - 15*a^3*b^2 - 19*a*b^4)*cos(d*x + c)^3 + 3*(a^3*b^2 + a*b^4)*cos(d*x + c) + (15*a^2*b^3 + 15*b^5 - 2*(2*a^4*b + 27*a^2*b^3 + 25*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^2*b^3 + b^5)*d*cos(d*x + c)^3)","B",0
504,1,1879,0,0.579889," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} b^{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} b^{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{2} - 15 \, \sqrt{2} {\left(a b^{2} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 15 \, \sqrt{2} {\left(a b^{2} d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{2} b^{2} + 3 \, b^{4} - 2 \, {\left(a^{4} + 10 \, a^{2} b^{2} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*b^2*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4))*cos(d*x + c)^2 + 60*sqrt(2)*b^2*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4))*cos(d*x + c)^2 - 15*sqrt(2)*(a*b^2*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c)^2 + (a^2*b^2 + b^4)*d*cos(d*x + c)^2)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 15*sqrt(2)*(a*b^2*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c)^2 + (a^2*b^2 + b^4)*d*cos(d*x + c)^2)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(3*a^2*b^2 + 3*b^4 - 2*(a^4 + 10*a^2*b^2 + 9*b^4)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^2*b^2 + b^4)*d*cos(d*x + c)^2)","B",0
505,1,1586,0,0.567499," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} b d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} b d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right) - 3 \, \sqrt{2} {\left(a b d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left(a b d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{2} b + b^{3}\right)} d \cos\left(d x + c\right)}"," ",0,"1/12*(12*sqrt(2)*b*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) + (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4))*cos(d*x + c) + 12*sqrt(2)*b*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) - (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4))*cos(d*x + c) - 3*sqrt(2)*(a*b*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^2*b + b^3)*d*cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 3*sqrt(2)*(a*b*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^2*b + b^3)*d*cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*((a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^2*b + b^3)*d*cos(d*x + c))","B",0
506,1,1740,0,0.520201," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left(a^{2} + b^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/4*(4*sqrt(2)*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4) + (a^2 + b^2)*d)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4) + (a^2 + b^2)*d)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(a^2 + b^2)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^2 + b^2)*d)","B",0
507,1,1465,0,0.485104," ","integrate((a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} d^{4} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} d^{4} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left(a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left(a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right)}{4 \, {\left(a^{2} + b^{2}\right)}}"," ",0,"-1/4*(4*sqrt(2)*d^4*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) + (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*d^4*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) - (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4)) - sqrt(2)*(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))))/(a^2 + b^2)","B",0
508,1,3585,0,1.513217," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 2 \, {\left(a^{2} + b^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}, -\frac{4 \, \sqrt{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(a^{2} + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}\right]"," ",0,"[-1/4*(4*sqrt(2)*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4) + (a^2 + b^2)*d)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4) + (a^2 + b^2)*d)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 2*(a^2 + b^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/((a^2 + b^2)*d), -1/4*(4*sqrt(2)*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*d^5*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4) + (a^2 + b^2)*d)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4) + (a^2 + b^2)*d)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(a^2 + b^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/((a^2 + b^2)*d)]","B",0
509,1,3539,0,1.295012," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, {\left(a^{3} + a b^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - {\left(a^{2} d^{3} \cos\left(d x + c\right)^{2} - a^{2} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - {\left(a^{2} d^{3} \cos\left(d x + c\right)^{2} - a^{2} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} b d^{5} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} d^{5} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, {\left(a^{3} + a b^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - {\left(a^{2} d^{3} \cos\left(d x + c\right)^{2} - a^{2} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - {\left(a^{2} d^{3} \cos\left(d x + c\right)^{2} - a^{2} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d^{3} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 4 \, {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) + (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) - (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4)) + 4*(a^3 + a*b^2)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - (a^2*d^3*cos(d*x + c)^2 - a^2*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - (a^2*d^3*cos(d*x + c)^2 - a^2*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - (a^2*b + b^3 - (a^2*b + b^3)*cos(d*x + c)^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d), 1/4*(4*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) + (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-(sqrt(2)*b*d^5*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*d^5*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*sqrt(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4) - (a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) - (a^3 + a*b^2)*d^2*sqrt(b^2/d^4))/(a^2*b^2 + b^4)) + 4*(a^3 + a*b^2)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - (a^2*d^3*cos(d*x + c)^2 - a^2*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log((sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c) + (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - (a^2*d^3*cos(d*x + c)^2 - a^2*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(-(sqrt(2)*b^3*d^3*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt((a*d^2*sqrt((a^2 + b^2)/d^4) + a^2 + b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - (a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 4*(a^2*b + b^3 - (a^2*b + b^3)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d)]","B",0
510,1,4130,0,1.411929," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{16 \, \sqrt{2} {\left(a^{2} d^{5} \cos\left(d x + c\right)^{2} - a^{2} d^{5}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) + 16 \, \sqrt{2} {\left(a^{2} d^{5} \cos\left(d x + c\right)^{2} - a^{2} d^{5}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) - 4 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 4 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - {\left(8 \, a^{4} + 9 \, a^{2} b^{2} + b^{4} - {\left(8 \, a^{4} + 9 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) + 4 \, {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{16 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left(a^{2} d^{5} \cos\left(d x + c\right)^{2} - a^{2} d^{5}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{2} d^{5} \cos\left(d x + c\right)^{2} - a^{2} d^{5}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{d^{4}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{b^{2}}{d^{4}}} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} + a d^{5} \sqrt{\frac{b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{3}{4}}}{a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}}\right)} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(a d^{3} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{a d^{2} \sqrt{\frac{a^{2} + b^{2}}{d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{a^{2} + b^{2}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + {\left(8 \, a^{4} + 9 \, a^{2} b^{2} + b^{4} - {\left(8 \, a^{4} + 9 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) + {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d\right)}}\right]"," ",0,"[1/16*(16*sqrt(2)*(a^2*d^5*cos(d*x + c)^2 - a^2*d^5)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) + 16*sqrt(2)*(a^2*d^5*cos(d*x + c)^2 - a^2*d^5)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) - 4*sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 4*sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - (8*a^4 + 9*a^2*b^2 + b^4 - (8*a^4 + 9*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 + 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) + 4*(2*(a^4 + a^2*b^2)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d), 1/4*(4*sqrt(2)*(a^2*d^5*cos(d*x + c)^2 - a^2*d^5)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(-((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) + 4*sqrt(2)*(a^2*d^5*cos(d*x + c)^2 - a^2*d^5)*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(b^2/d^4)*((a^2 + b^2)/d^4)^(3/4)*arctan(((a^2 + b^2)*d^4*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + (a^3 + a*b^2)*d^2*sqrt(b^2/d^4) - sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt(b^2/d^4)*sqrt((a^2 + b^2)/d^4) + a*d^5*sqrt(b^2/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*sqrt(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^2 + b^2)/d^4)^(3/4))/(a^2*b^2 + b^4)) - sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt((a^2 + b^2)/d^4))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4)*log(((a^2 + b^2)*d^2*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) - sqrt(2)*(a*d^3*sqrt((a^2 + b^2)/d^4)*cos(d*x + c) + (a^2 + b^2)*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-(a*d^2*sqrt((a^2 + b^2)/d^4) - a^2 - b^2)/b^2)*((a^2 + b^2)/d^4)^(1/4) + (a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + (8*a^4 + 9*a^2*b^2 + b^4 - (8*a^4 + 9*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) + (2*(a^4 + a^2*b^2)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d)]","B",0
511,1,4429,0,1.185421," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{1260 \, \sqrt{2} b^{3} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right)^{4} + 1260 \, \sqrt{2} b^{3} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right)^{4} + 315 \, \sqrt{2} {\left({\left(a^{3} b^{3} - 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right)^{4} - {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 315 \, \sqrt{2} {\left({\left(a^{3} b^{3} - 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right)^{4} - {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left(35 \, a^{6} b^{4} + 105 \, a^{4} b^{6} + 105 \, a^{2} b^{8} + 35 \, b^{10} + {\left(8 \, a^{10} - 42 \, a^{8} b^{2} + 239 \, a^{6} b^{4} + 1049 \, a^{4} b^{6} + 1173 \, a^{2} b^{8} + 413 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{8} b^{2} - 124 \, a^{6} b^{4} - 390 \, a^{4} b^{6} - 396 \, a^{2} b^{8} - 133 \, b^{10}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{9} b + 47 \, a^{7} b^{3} + 135 \, a^{5} b^{5} + 133 \, a^{3} b^{7} + 44 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 25 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{1260 \, {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/1260*(1260*sqrt(2)*b^3*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c)^4 + 1260*sqrt(2)*b^3*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c)^4 + 315*sqrt(2)*((a^3*b^3 - 3*a*b^5)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c)^4 - (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*cos(d*x + c)^4)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 315*sqrt(2)*((a^3*b^3 - 3*a*b^5)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c)^4 - (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*cos(d*x + c)^4)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(35*a^6*b^4 + 105*a^4*b^6 + 105*a^2*b^8 + 35*b^10 + (8*a^10 - 42*a^8*b^2 + 239*a^6*b^4 + 1049*a^4*b^6 + 1173*a^2*b^8 + 413*b^10)*cos(d*x + c)^4 + (3*a^8*b^2 - 124*a^6*b^4 - 390*a^4*b^6 - 396*a^2*b^8 - 133*b^10)*cos(d*x + c)^2 - 2*(2*(a^9*b + 47*a^7*b^3 + 135*a^5*b^5 + 133*a^3*b^7 + 44*a*b^9)*cos(d*x + c)^3 - 25*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d*cos(d*x + c)^4)","B",0
512,1,4373,0,1.276453," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{420 \, \sqrt{2} b^{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} b^{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right)^{3} + 105 \, \sqrt{2} {\left({\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 105 \, \sqrt{2} {\left({\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(2 \, {\left(3 \, a^{9} + 91 \, a^{7} b^{2} + 255 \, a^{5} b^{4} + 249 \, a^{3} b^{6} + 82 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) - {\left(15 \, a^{6} b^{3} + 45 \, a^{4} b^{5} + 45 \, a^{2} b^{7} + 15 \, b^{9} + {\left(3 \, a^{8} b - 41 \, a^{6} b^{3} - 141 \, a^{4} b^{5} - 147 \, a^{2} b^{7} - 50 \, b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{420 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"1/420*(420*sqrt(2)*b^2*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c)^3 + 420*sqrt(2)*b^2*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c)^3 + 105*sqrt(2)*((a^3*b^2 - 3*a*b^4)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c)^3 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*cos(d*x + c)^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 105*sqrt(2)*((a^3*b^2 - 3*a*b^4)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c)^3 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*cos(d*x + c)^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(2*(3*a^9 + 91*a^7*b^2 + 255*a^5*b^4 + 249*a^3*b^6 + 82*a*b^8)*cos(d*x + c)^3 - 24*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*cos(d*x + c) - (15*a^6*b^3 + 45*a^4*b^5 + 45*a^2*b^7 + 15*b^9 + (3*a^8*b - 41*a^6*b^3 - 141*a^4*b^5 - 147*a^2*b^7 - 50*b^9)*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d*cos(d*x + c)^3)","B",0
513,1,4304,0,1.236871," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} b d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right)^{2} + 20 \, \sqrt{2} b d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right)^{2} + 5 \, \sqrt{2} {\left({\left(a^{3} b - 3 \, a b^{3}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 5 \, \sqrt{2} {\left({\left(a^{3} b - 3 \, a b^{3}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8} + {\left(a^{8} - 3 \, a^{6} b^{2} - 15 \, a^{4} b^{4} - 17 \, a^{2} b^{6} - 6 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{20 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/20*(20*sqrt(2)*b*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c)^2 + 20*sqrt(2)*b*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c)^2 + 5*sqrt(2)*((a^3*b - 3*a*b^3)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c)^2 - (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*cos(d*x + c)^2)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 5*sqrt(2)*((a^3*b - 3*a*b^3)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c)^2 - (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*cos(d*x + c)^2)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8 + (a^8 - 3*a^6*b^2 - 15*a^4*b^4 - 17*a^2*b^6 - 6*b^8)*cos(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*cos(d*x + c)^2)","B",0
514,1,4234,0,1.378042," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(4 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c) + 12*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16))*cos(d*x + c) + 3*sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 3*sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(4*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c))","B",0
515,1,4150,0,1.213147," ","integrate((a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/4*(4*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4) - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4) - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","B",0
516,1,8401,0,2.782588," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}, \frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}\right]"," ",0,"[1/4*(4*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d), 1/4*(4*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*d^5*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^3 - 3*a*b^2)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4) + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)]","B",0
517,1,8973,0,2.851863," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) - 4 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d - {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d - {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 3 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7} - {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)}}, -\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(3 \, a^{7} b + 5 \, a^{5} b^{3} + a^{3} b^{5} - a b^{7}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) - 4 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d - {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d - {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} b^{2} + 21 \, a^{9} b^{4} + 10 \, a^{7} b^{6} - 6 \, a^{5} b^{8} - 3 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b^{3} + 21 \, a^{8} b^{5} + 10 \, a^{6} b^{7} - 6 \, a^{4} b^{9} - 3 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 12 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7} - {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left({\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) - 4*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d - ((a^3 - 3*a*b^2)*d^3*cos(d*x + c)^2 - (a^3 - 3*a*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d - ((a^3 - 3*a*b^2)*d^3*cos(d*x + c)^2 - (a^3 - 3*a*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 3*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7 - (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d), -1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^4*b + 2*a^2*b^3 - b^5)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(3*a^7*b + 5*a^5*b^3 + a^3*b^5 - a*b^7)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + 2*(a^3 + a*b^2)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) - 4*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d - ((a^3 - 3*a*b^2)*d^3*cos(d*x + c)^2 - (a^3 - 3*a*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + sqrt(2)*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d - ((a^3 - 3*a*b^2)*d^3*cos(d*x + c)^2 - (a^3 - 3*a*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*(2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11*b^2 + 21*a^9*b^4 + 10*a^7*b^6 - 6*a^5*b^8 - 3*a^3*b^10 + a*b^12)*cos(d*x + c) + (9*a^10*b^3 + 21*a^8*b^5 + 10*a^6*b^7 - 6*a^4*b^9 - 3*a^2*b^11 + b^13)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 12*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7 - (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)]","B",0
518,1,9142,0,3.052110," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{16 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 16 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d + {\left({\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 4 \, \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d + {\left({\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - {\left(8 \, a^{8} + 21 \, a^{6} b^{2} + 15 \, a^{4} b^{4} - a^{2} b^{6} - 3 \, b^{8} - {\left(8 \, a^{8} + 21 \, a^{6} b^{2} + 15 \, a^{4} b^{4} - a^{2} b^{6} - 3 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) - 4 \, {\left(2 \, {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{16 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}, -\frac{4 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + 4 \, \sqrt{2} {\left(a d^{5} \cos\left(d x + c\right)^{2} - a d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} \arctan\left(-\frac{{\left(3 \, a^{10} + 11 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - a^{2} b^{8} - b^{10}\right)} d^{4} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{5} + 2 \, a^{3} b^{2} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(3 \, a^{8} + 2 \, a^{6} b^{2} - 4 \, a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}} + {\left(a^{4} - b^{4}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{14} b^{2} + 39 \, a^{12} b^{4} + 61 \, a^{10} b^{6} + 35 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 11 \, a^{4} b^{12} - a^{2} b^{14} + b^{16}}\right) + \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d + {\left({\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d + {\left({\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{3}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d^{3} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}{d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{11} + 21 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 6 \, a^{5} b^{6} - 3 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{10} b + 21 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 6 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - {\left(8 \, a^{8} + 21 \, a^{6} b^{2} + 15 \, a^{4} b^{4} - a^{2} b^{6} - 3 \, b^{8} - {\left(8 \, a^{8} + 21 \, a^{6} b^{2} + 15 \, a^{4} b^{4} - a^{2} b^{6} - 3 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - {\left(2 \, {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}\right]"," ",0,"[-1/16*(16*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 16*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d + ((a^4 - 3*a^2*b^2)*d^3*cos(d*x + c)^2 - (a^4 - 3*a^2*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 4*sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d + ((a^4 - 3*a^2*b^2)*d^3*cos(d*x + c)^2 - (a^4 - 3*a^2*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - (8*a^8 + 21*a^6*b^2 + 15*a^4*b^4 - a^2*b^6 - 3*b^8 - (8*a^8 + 21*a^6*b^2 + 15*a^4*b^4 - a^2*b^6 - 3*b^8)*cos(d*x + c)^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) - 4*(2*(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*cos(d*x + c)^2 + 5*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d), -1/4*(4*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) + sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + 4*sqrt(2)*(a*d^5*cos(d*x + c)^2 - a*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4)*arctan(-((3*a^10 + 11*a^8*b^2 + 14*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10)*d^4*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) - sqrt(2)*((3*a^5 + 2*a^3*b^2 - a*b^4)*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (3*a^8 + 2*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 + b^8)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4) - sqrt(2)*(a*d^7*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4) + (a^4 - b^4)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(3/4))/(9*a^14*b^2 + 39*a^12*b^4 + 61*a^10*b^6 + 35*a^8*b^8 - 5*a^6*b^10 - 11*a^4*b^12 - a^2*b^14 + b^16)) + sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d + ((a^4 - 3*a^2*b^2)*d^3*cos(d*x + c)^2 - (a^4 - 3*a^2*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d + ((a^4 - 3*a^2*b^2)*d^3*cos(d*x + c)^2 - (a^4 - 3*a^2*b^2)*d^3)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) - sqrt(2)*((9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d^3*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)*cos(d*x + c) + (9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^3 - 3*a*b^2)*d^2*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/d^4)^(1/4) + (9*a^11 + 21*a^9*b^2 + 10*a^7*b^4 - 6*a^5*b^6 - 3*a^3*b^8 + a*b^10)*cos(d*x + c) + (9*a^10*b + 21*a^8*b^3 + 10*a^6*b^5 - 6*a^4*b^7 - 3*a^2*b^9 + b^11)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - (8*a^8 + 21*a^6*b^2 + 15*a^4*b^4 - a^2*b^6 - 3*b^8 - (8*a^8 + 21*a^6*b^2 + 15*a^4*b^4 - a^2*b^6 - 3*b^8)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) - (2*(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*cos(d*x + c)^2 + 5*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d)]","B",0
519,1,6847,0,4.904390," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{1260 \, \sqrt{2} b^{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right)^{4} + 1260 \, \sqrt{2} b^{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right)^{4} + 315 \, \sqrt{2} {\left({\left(a^{5} b^{2} - 10 \, a^{3} b^{4} + 5 \, a b^{6}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right)^{4} + {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 315 \, \sqrt{2} {\left({\left(a^{5} b^{2} - 10 \, a^{3} b^{4} + 5 \, a b^{6}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right)^{4} + {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left(35 \, a^{10} b^{4} + 175 \, a^{8} b^{6} + 350 \, a^{6} b^{8} + 350 \, a^{4} b^{10} + 175 \, a^{2} b^{12} + 35 \, b^{14} - {\left(10 \, a^{14} + 608 \, a^{12} b^{2} + 2477 \, a^{10} b^{4} + 3615 \, a^{8} b^{6} + 1500 \, a^{6} b^{8} - 1330 \, a^{4} b^{10} - 1507 \, a^{2} b^{12} - 413 \, b^{14}\right)} \cos\left(d x + c\right)^{4} + {\left(75 \, a^{12} b^{2} + 242 \, a^{10} b^{4} + 85 \, a^{8} b^{6} - 580 \, a^{6} b^{8} - 955 \, a^{4} b^{10} - 590 \, a^{2} b^{12} - 133 \, b^{14}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(5 \, a^{13} b - 301 \, a^{11} b^{3} - 1580 \, a^{9} b^{5} - 3210 \, a^{7} b^{7} - 3235 \, a^{5} b^{9} - 1625 \, a^{3} b^{11} - 326 \, a b^{13}\right)} \cos\left(d x + c\right)^{3} + 95 \, {\left(a^{11} b^{3} + 5 \, a^{9} b^{5} + 10 \, a^{7} b^{7} + 10 \, a^{5} b^{9} + 5 \, a^{3} b^{11} + a b^{13}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{1260 \, {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/1260*(1260*sqrt(2)*b^2*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c)^4 + 1260*sqrt(2)*b^2*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c)^4 + 315*sqrt(2)*((a^5*b^2 - 10*a^3*b^4 + 5*a*b^6)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c)^4 + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*d*cos(d*x + c)^4)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 315*sqrt(2)*((a^5*b^2 - 10*a^3*b^4 + 5*a*b^6)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c)^4 + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*d*cos(d*x + c)^4)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(35*a^10*b^4 + 175*a^8*b^6 + 350*a^6*b^8 + 350*a^4*b^10 + 175*a^2*b^12 + 35*b^14 - (10*a^14 + 608*a^12*b^2 + 2477*a^10*b^4 + 3615*a^8*b^6 + 1500*a^6*b^8 - 1330*a^4*b^10 - 1507*a^2*b^12 - 413*b^14)*cos(d*x + c)^4 + (75*a^12*b^2 + 242*a^10*b^4 + 85*a^8*b^6 - 580*a^6*b^8 - 955*a^4*b^10 - 590*a^2*b^12 - 133*b^14)*cos(d*x + c)^2 + ((5*a^13*b - 301*a^11*b^3 - 1580*a^9*b^5 - 3210*a^7*b^7 - 3235*a^5*b^9 - 1625*a^3*b^11 - 326*a*b^13)*cos(d*x + c)^3 + 95*(a^11*b^3 + 5*a^9*b^5 + 10*a^7*b^7 + 10*a^5*b^9 + 5*a^3*b^11 + a*b^13)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*d*cos(d*x + c)^4)","B",0
520,1,6733,0,5.154275," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{84 \, \sqrt{2} b d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right)^{3} + 84 \, \sqrt{2} b d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right)^{3} - 21 \, \sqrt{2} {\left({\left(a^{5} b - 10 \, a^{3} b^{3} + 5 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left(a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 21 \, \sqrt{2} {\left({\left(a^{5} b - 10 \, a^{3} b^{3} + 5 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left(a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left({\left(3 \, a^{13} - 43 \, a^{11} b^{2} - 260 \, a^{9} b^{4} - 550 \, a^{7} b^{6} - 565 \, a^{5} b^{8} - 287 \, a^{3} b^{10} - 58 \, a b^{12}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(a^{11} b^{2} + 5 \, a^{9} b^{4} + 10 \, a^{7} b^{6} + 10 \, a^{5} b^{8} + 5 \, a^{3} b^{10} + a b^{12}\right)} \cos\left(d x + c\right) + {\left(3 \, a^{10} b^{3} + 15 \, a^{8} b^{5} + 30 \, a^{6} b^{7} + 30 \, a^{4} b^{9} + 15 \, a^{2} b^{11} + 3 \, b^{13} + {\left(9 \, a^{12} b + 35 \, a^{10} b^{3} + 40 \, a^{8} b^{5} - 10 \, a^{6} b^{7} - 55 \, a^{4} b^{9} - 41 \, a^{2} b^{11} - 10 \, b^{13}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{84 \, {\left(a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"1/84*(84*sqrt(2)*b*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c)^3 + 84*sqrt(2)*b*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c)^3 - 21*sqrt(2)*((a^5*b - 10*a^3*b^3 + 5*a*b^5)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c)^3 - (a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11)*d*cos(d*x + c)^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 21*sqrt(2)*((a^5*b - 10*a^3*b^3 + 5*a*b^5)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c)^3 - (a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11)*d*cos(d*x + c)^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*((3*a^13 - 43*a^11*b^2 - 260*a^9*b^4 - 550*a^7*b^6 - 565*a^5*b^8 - 287*a^3*b^10 - 58*a*b^12)*cos(d*x + c)^3 + 9*(a^11*b^2 + 5*a^9*b^4 + 10*a^7*b^6 + 10*a^5*b^8 + 5*a^3*b^10 + a*b^12)*cos(d*x + c) + (3*a^10*b^3 + 15*a^8*b^5 + 30*a^6*b^7 + 30*a^4*b^9 + 15*a^2*b^11 + 3*b^13 + (9*a^12*b + 35*a^10*b^3 + 40*a^8*b^5 - 10*a^6*b^7 - 55*a^4*b^9 - 41*a^2*b^11 - 10*b^13)*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11)*d*cos(d*x + c)^3)","B",0
521,1,6683,0,4.949847," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right)^{2} + 15 \, \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 30 \, a^{6} b^{6} + 30 \, a^{4} b^{8} + 15 \, a^{2} b^{10} + 3 \, b^{12} + {\left(23 \, a^{12} + 97 \, a^{10} b^{2} + 140 \, a^{8} b^{4} + 50 \, a^{6} b^{6} - 65 \, a^{4} b^{8} - 67 \, a^{2} b^{10} - 18 \, b^{12}\right)} \cos\left(d x + c\right)^{2} + 11 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c)^2 + 60*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c)^2 + 15*sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c)^2 + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 15*sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c)^2 + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(3*a^10*b^2 + 15*a^8*b^4 + 30*a^6*b^6 + 30*a^4*b^8 + 15*a^2*b^10 + 3*b^12 + (23*a^12 + 97*a^10*b^2 + 140*a^8*b^4 + 50*a^6*b^6 - 65*a^4*b^8 - 67*a^2*b^10 - 18*b^12)*cos(d*x + c)^2 + 11*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2)","B",0
522,1,6582,0,4.793518," ","integrate((a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) \cos\left(d x + c\right) - 3 \, \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(7 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right) + {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c) + 12*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28))*cos(d*x + c) - 3*sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 3*sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(7*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(d*x + c) + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c))","B",0
523,1,13263,0,9.517662," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 2 \, {\left(a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) + 8 \, {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d}, \frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 8 \, {\left(a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) + 8 \, {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d}\right]"," ",0,"[1/4*(4*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 2*(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) + 8*(a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d), 1/4*(4*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*sqrt(2)*d^5*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 8*(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) + 8*(a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)]","B",0
524,1,13829,0,10.493303," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, {\left(a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d - {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d - {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 5 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11} - {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left(2 \, {\left(5 \, a^{9} b - 14 \, a^{5} b^{5} - 8 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(15 \, a^{14} b + 25 \, a^{12} b^{3} - 37 \, a^{10} b^{5} - 99 \, a^{8} b^{7} - 51 \, a^{6} b^{9} + 11 \, a^{4} b^{11} + 9 \, a^{2} b^{13} - b^{15}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, a d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(3 \, a^{6} + 5 \, a^{4} b^{2} + a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, {\left(a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d - {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d - {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} b^{2} + 25 \, a^{17} b^{4} - 140 \, a^{15} b^{6} - 220 \, a^{13} b^{8} + 126 \, a^{11} b^{10} + 430 \, a^{9} b^{12} + 260 \, a^{7} b^{14} + 20 \, a^{5} b^{16} - 15 \, a^{3} b^{18} + a b^{20}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b^{3} + 25 \, a^{16} b^{5} - 140 \, a^{14} b^{7} - 220 \, a^{12} b^{9} + 126 \, a^{10} b^{11} + 430 \, a^{8} b^{13} + 260 \, a^{6} b^{15} + 20 \, a^{4} b^{17} - 15 \, a^{2} b^{19} + b^{21}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 20 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11} - {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d - ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d - ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 5*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11 - (a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(d*x + c)^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d), 1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*(2*(5*a^9*b - 14*a^5*b^5 - 8*a^3*b^7 + a*b^9)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (15*a^14*b + 25*a^12*b^3 - 37*a^10*b^5 - 99*a^8*b^7 - 51*a^6*b^9 + 11*a^4*b^11 + 9*a^2*b^13 - b^15)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*(2*a*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (3*a^6 + 5*a^4*b^2 + a^2*b^4 - b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d - ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d - ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + 2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19*b^2 + 25*a^17*b^4 - 140*a^15*b^6 - 220*a^13*b^8 + 126*a^11*b^10 + 430*a^9*b^12 + 260*a^7*b^14 + 20*a^5*b^16 - 15*a^3*b^18 + a*b^20)*cos(d*x + c) + (25*a^18*b^3 + 25*a^16*b^5 - 140*a^14*b^7 - 220*a^12*b^9 + 126*a^10*b^11 + 430*a^8*b^13 + 260*a^6*b^15 + 20*a^4*b^17 - 15*a^2*b^19 + b^21)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 20*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11 - (a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)]","B",0
525,1,14030,0,10.704450," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{16 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 16 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d + {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 4 \, \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d + {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - {\left(8 \, a^{12} + 25 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 70 \, a^{6} b^{6} - 110 \, a^{4} b^{8} - 67 \, a^{2} b^{10} - 15 \, b^{12} - {\left(8 \, a^{12} + 25 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 70 \, a^{6} b^{6} - 110 \, a^{4} b^{8} - 67 \, a^{2} b^{10} - 15 \, b^{12}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) - 4 \, {\left(2 \, {\left(a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{16 \, {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)}}, -\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} \arctan\left(-\frac{{\left(5 \, a^{18} + 25 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 28 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 210 \, a^{8} b^{10} - 140 \, a^{6} b^{12} - 44 \, a^{4} b^{14} - 3 \, a^{2} b^{16} + b^{18}\right)} d^{4} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{23} + 35 \, a^{21} b^{2} + 91 \, a^{19} b^{4} + 69 \, a^{17} b^{6} - 174 \, a^{15} b^{8} - 546 \, a^{13} b^{10} - 714 \, a^{11} b^{12} - 534 \, a^{9} b^{14} - 231 \, a^{7} b^{16} - 49 \, a^{5} b^{18} - a^{3} b^{20} + a b^{22}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} - \sqrt{2} {\left({\left(5 \, a^{10} - 5 \, a^{8} b^{2} - 14 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 9 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(5 \, a^{15} - 5 \, a^{13} b^{2} - 39 \, a^{11} b^{4} - 9 \, a^{9} b^{6} + 79 \, a^{7} b^{8} + 81 \, a^{5} b^{10} + 19 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}} + {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{26} b^{2} + 125 \, a^{24} b^{4} + 110 \, a^{22} b^{6} - 530 \, a^{20} b^{8} - 1469 \, a^{18} b^{10} - 921 \, a^{16} b^{12} + 1716 \, a^{14} b^{14} + 3924 \, a^{12} b^{16} + 3471 \, a^{10} b^{18} + 1531 \, a^{8} b^{20} + 254 \, a^{6} b^{22} - 34 \, a^{4} b^{24} - 11 \, a^{2} b^{26} + b^{28}}\right) + \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d + {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d + {\left({\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{3}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d^{2} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}}{d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{19} + 25 \, a^{17} b^{2} - 140 \, a^{15} b^{4} - 220 \, a^{13} b^{6} + 126 \, a^{11} b^{8} + 430 \, a^{9} b^{10} + 260 \, a^{7} b^{12} + 20 \, a^{5} b^{14} - 15 \, a^{3} b^{16} + a b^{18}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{18} b + 25 \, a^{16} b^{3} - 140 \, a^{14} b^{5} - 220 \, a^{12} b^{7} + 126 \, a^{10} b^{9} + 430 \, a^{8} b^{11} + 260 \, a^{6} b^{13} + 20 \, a^{4} b^{15} - 15 \, a^{2} b^{17} + b^{19}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - {\left(8 \, a^{12} + 25 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 70 \, a^{6} b^{6} - 110 \, a^{4} b^{8} - 67 \, a^{2} b^{10} - 15 \, b^{12} - {\left(8 \, a^{12} + 25 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 70 \, a^{6} b^{6} - 110 \, a^{4} b^{8} - 67 \, a^{2} b^{10} - 15 \, b^{12}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - {\left(2 \, {\left(a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d\right)}}\right]"," ",0,"[-1/16*(16*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 16*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d + ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 4*sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d + ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - (8*a^12 + 25*a^10*b^2 + 5*a^8*b^4 - 70*a^6*b^6 - 110*a^4*b^8 - 67*a^2*b^10 - 15*b^12 - (8*a^12 + 25*a^10*b^2 + 5*a^8*b^4 - 70*a^6*b^6 - 110*a^4*b^8 - 67*a^2*b^10 - 15*b^12)*cos(d*x + c)^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) - 4*(2*(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10)*cos(d*x + c)^2 + 9*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d), -1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4)*arctan(-((5*a^18 + 25*a^16*b^2 + 36*a^14*b^4 - 28*a^12*b^6 - 154*a^10*b^8 - 210*a^8*b^10 - 140*a^6*b^12 - 44*a^4*b^14 - 3*a^2*b^16 + b^18)*d^4*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^23 + 35*a^21*b^2 + 91*a^19*b^4 + 69*a^17*b^6 - 174*a^15*b^8 - 546*a^13*b^10 - 714*a^11*b^12 - 534*a^9*b^14 - 231*a^7*b^16 - 49*a^5*b^18 - a^3*b^20 + a*b^22)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) - sqrt(2)*((5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 6*a^4*b^6 + 9*a^2*b^8 - b^10)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (5*a^15 - 5*a^13*b^2 - 39*a^11*b^4 - 9*a^9*b^6 + 79*a^7*b^8 + 81*a^5*b^10 + 19*a^3*b^12 - 3*a*b^14)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4) + (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(3/4))/(25*a^26*b^2 + 125*a^24*b^4 + 110*a^22*b^6 - 530*a^20*b^8 - 1469*a^18*b^10 - 921*a^16*b^12 + 1716*a^14*b^14 + 3924*a^12*b^16 + 3471*a^10*b^18 + 1531*a^8*b^20 + 254*a^6*b^22 - 34*a^4*b^24 - 11*a^2*b^26 + b^28)) + sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d + ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - sqrt(2)*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d + ((a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3*cos(d*x + c)^2 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^3)*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) - sqrt(2)*((25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d^3*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)*cos(d*x + c) + (25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^5 - 10*a^3*b^2 + 5*a*b^4)*d^2*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)/d^4)^(1/4) + (25*a^19 + 25*a^17*b^2 - 140*a^15*b^4 - 220*a^13*b^6 + 126*a^11*b^8 + 430*a^9*b^10 + 260*a^7*b^12 + 20*a^5*b^14 - 15*a^3*b^16 + a*b^18)*cos(d*x + c) + (25*a^18*b + 25*a^16*b^3 - 140*a^14*b^5 - 220*a^12*b^7 + 126*a^10*b^9 + 430*a^8*b^11 + 260*a^6*b^13 + 20*a^4*b^15 - 15*a^2*b^17 + b^19)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - (8*a^12 + 25*a^10*b^2 + 5*a^8*b^4 - 70*a^6*b^6 - 110*a^4*b^8 - 67*a^2*b^10 - 15*b^12 - (8*a^12 + 25*a^10*b^2 + 5*a^8*b^4 - 70*a^6*b^6 - 110*a^4*b^8 - 67*a^2*b^10 - 15*b^12)*cos(d*x + c)^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) - (2*(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10)*cos(d*x + c)^2 + 9*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d)]","B",0
526,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,1,9021,0,27.250266," ","integrate((a+b*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} d^{5} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} \arctan\left(-\frac{{\left(7 \, a^{26} + 35 \, a^{24} b^{2} - 14 \, a^{22} b^{4} - 526 \, a^{20} b^{6} - 1795 \, a^{18} b^{8} - 3111 \, a^{16} b^{10} - 3060 \, a^{14} b^{12} - 1428 \, a^{12} b^{14} + 273 \, a^{10} b^{16} + 805 \, a^{8} b^{18} + 482 \, a^{6} b^{20} + 130 \, a^{4} b^{22} + 11 \, a^{2} b^{24} - b^{26}\right)} d^{4} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + {\left(7 \, a^{33} + 56 \, a^{31} b^{2} + 112 \, a^{29} b^{4} - 456 \, a^{27} b^{6} - 3380 \, a^{25} b^{8} - 10088 \, a^{23} b^{10} - 18304 \, a^{21} b^{12} - 21736 \, a^{19} b^{14} - 16302 \, a^{17} b^{16} - 5720 \, a^{15} b^{18} + 2288 \, a^{13} b^{20} + 4264 \, a^{11} b^{22} + 2652 \, a^{9} b^{24} + 904 \, a^{7} b^{26} + 160 \, a^{5} b^{28} + 8 \, a^{3} b^{30} - a b^{32}\right)} d^{2} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + \sqrt{2} {\left({\left(21 \, a^{14} b - 49 \, a^{12} b^{3} - 175 \, a^{10} b^{5} - 45 \, a^{8} b^{7} + 111 \, a^{6} b^{9} + 29 \, a^{4} b^{11} - 21 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 4 \, {\left(7 \, a^{21} b - 91 \, a^{17} b^{5} - 176 \, a^{15} b^{7} - 26 \, a^{13} b^{9} + 208 \, a^{11} b^{11} + 170 \, a^{9} b^{13} - 16 \, a^{7} b^{15} - 61 \, a^{5} b^{17} - 16 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}}\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 4 \, {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}}\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{{\left(49 \, a^{20} b^{2} - 294 \, a^{18} b^{4} - 147 \, a^{16} b^{6} + 1848 \, a^{14} b^{8} + 1778 \, a^{12} b^{10} - 1316 \, a^{10} b^{12} - 1518 \, a^{8} b^{14} + 312 \, a^{6} b^{16} + 349 \, a^{4} b^{18} - 38 \, a^{2} b^{20} + b^{22}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(4 \, {\left(49 \, a^{15} b^{3} - 539 \, a^{13} b^{5} + 2009 \, a^{11} b^{7} - 3003 \, a^{9} b^{9} + 1995 \, a^{7} b^{11} - 553 \, a^{5} b^{13} + 43 \, a^{3} b^{15} - a b^{17}\right)} d^{3} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) + {\left(147 \, a^{22} b^{3} - 931 \, a^{20} b^{5} - 147 \, a^{18} b^{7} + 5691 \, a^{16} b^{9} + 3486 \, a^{14} b^{11} - 5726 \, a^{12} b^{13} - 3238 \, a^{10} b^{15} + 2454 \, a^{8} b^{17} + 735 \, a^{6} b^{19} - 463 \, a^{4} b^{21} + 41 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{27} b^{2} - 147 \, a^{25} b^{4} - 882 \, a^{23} b^{6} + 574 \, a^{21} b^{8} + 6587 \, a^{19} b^{10} + 9415 \, a^{17} b^{12} + 1716 \, a^{15} b^{14} - 6412 \, a^{13} b^{16} - 4585 \, a^{11} b^{18} + 427 \, a^{9} b^{20} + 1246 \, a^{7} b^{22} + 238 \, a^{5} b^{24} - 35 \, a^{3} b^{26} + a b^{28}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{26} b^{3} - 147 \, a^{24} b^{5} - 882 \, a^{22} b^{7} + 574 \, a^{20} b^{9} + 6587 \, a^{18} b^{11} + 9415 \, a^{16} b^{13} + 1716 \, a^{14} b^{15} - 6412 \, a^{12} b^{17} - 4585 \, a^{10} b^{19} + 427 \, a^{8} b^{21} + 1246 \, a^{6} b^{23} + 238 \, a^{4} b^{25} - 35 \, a^{2} b^{27} + b^{29}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{3}{4}}}{49 \, a^{38} b^{2} + 147 \, a^{36} b^{4} - 1029 \, a^{34} b^{6} - 5943 \, a^{32} b^{8} - 5404 \, a^{30} b^{10} + 37996 \, a^{28} b^{12} + 154428 \, a^{26} b^{14} + 280020 \, a^{24} b^{16} + 272350 \, a^{22} b^{18} + 92378 \, a^{20} b^{20} - 104390 \, a^{18} b^{22} - 154050 \, a^{16} b^{24} - 76908 \, a^{14} b^{26} + 764 \, a^{12} b^{28} + 20908 \, a^{10} b^{30} + 10788 \, a^{8} b^{32} + 2169 \, a^{6} b^{34} + 43 \, a^{4} b^{36} - 29 \, a^{2} b^{38} + b^{40}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} d^{5} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} \arctan\left(\frac{{\left(7 \, a^{26} + 35 \, a^{24} b^{2} - 14 \, a^{22} b^{4} - 526 \, a^{20} b^{6} - 1795 \, a^{18} b^{8} - 3111 \, a^{16} b^{10} - 3060 \, a^{14} b^{12} - 1428 \, a^{12} b^{14} + 273 \, a^{10} b^{16} + 805 \, a^{8} b^{18} + 482 \, a^{6} b^{20} + 130 \, a^{4} b^{22} + 11 \, a^{2} b^{24} - b^{26}\right)} d^{4} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + {\left(7 \, a^{33} + 56 \, a^{31} b^{2} + 112 \, a^{29} b^{4} - 456 \, a^{27} b^{6} - 3380 \, a^{25} b^{8} - 10088 \, a^{23} b^{10} - 18304 \, a^{21} b^{12} - 21736 \, a^{19} b^{14} - 16302 \, a^{17} b^{16} - 5720 \, a^{15} b^{18} + 2288 \, a^{13} b^{20} + 4264 \, a^{11} b^{22} + 2652 \, a^{9} b^{24} + 904 \, a^{7} b^{26} + 160 \, a^{5} b^{28} + 8 \, a^{3} b^{30} - a b^{32}\right)} d^{2} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} - \sqrt{2} {\left({\left(21 \, a^{14} b - 49 \, a^{12} b^{3} - 175 \, a^{10} b^{5} - 45 \, a^{8} b^{7} + 111 \, a^{6} b^{9} + 29 \, a^{4} b^{11} - 21 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 4 \, {\left(7 \, a^{21} b - 91 \, a^{17} b^{5} - 176 \, a^{15} b^{7} - 26 \, a^{13} b^{9} + 208 \, a^{11} b^{11} + 170 \, a^{9} b^{13} - 16 \, a^{7} b^{15} - 61 \, a^{5} b^{17} - 16 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}}\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}} + 4 \, {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}{d^{4}}}\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{{\left(49 \, a^{20} b^{2} - 294 \, a^{18} b^{4} - 147 \, a^{16} b^{6} + 1848 \, a^{14} b^{8} + 1778 \, a^{12} b^{10} - 1316 \, a^{10} b^{12} - 1518 \, a^{8} b^{14} + 312 \, a^{6} b^{16} + 349 \, a^{4} b^{18} - 38 \, a^{2} b^{20} + b^{22}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(4 \, {\left(49 \, a^{15} b^{3} - 539 \, a^{13} b^{5} + 2009 \, a^{11} b^{7} - 3003 \, a^{9} b^{9} + 1995 \, a^{7} b^{11} - 553 \, a^{5} b^{13} + 43 \, a^{3} b^{15} - a b^{17}\right)} d^{3} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) + {\left(147 \, a^{22} b^{3} - 931 \, a^{20} b^{5} - 147 \, a^{18} b^{7} + 5691 \, a^{16} b^{9} + 3486 \, a^{14} b^{11} - 5726 \, a^{12} b^{13} - 3238 \, a^{10} b^{15} + 2454 \, a^{8} b^{17} + 735 \, a^{6} b^{19} - 463 \, a^{4} b^{21} + 41 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{27} b^{2} - 147 \, a^{25} b^{4} - 882 \, a^{23} b^{6} + 574 \, a^{21} b^{8} + 6587 \, a^{19} b^{10} + 9415 \, a^{17} b^{12} + 1716 \, a^{15} b^{14} - 6412 \, a^{13} b^{16} - 4585 \, a^{11} b^{18} + 427 \, a^{9} b^{20} + 1246 \, a^{7} b^{22} + 238 \, a^{5} b^{24} - 35 \, a^{3} b^{26} + a b^{28}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{26} b^{3} - 147 \, a^{24} b^{5} - 882 \, a^{22} b^{7} + 574 \, a^{20} b^{9} + 6587 \, a^{18} b^{11} + 9415 \, a^{16} b^{13} + 1716 \, a^{14} b^{15} - 6412 \, a^{12} b^{17} - 4585 \, a^{10} b^{19} + 427 \, a^{8} b^{21} + 1246 \, a^{6} b^{23} + 238 \, a^{4} b^{25} - 35 \, a^{2} b^{27} + b^{29}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{3}{4}}}{49 \, a^{38} b^{2} + 147 \, a^{36} b^{4} - 1029 \, a^{34} b^{6} - 5943 \, a^{32} b^{8} - 5404 \, a^{30} b^{10} + 37996 \, a^{28} b^{12} + 154428 \, a^{26} b^{14} + 280020 \, a^{24} b^{16} + 272350 \, a^{22} b^{18} + 92378 \, a^{20} b^{20} - 104390 \, a^{18} b^{22} - 154050 \, a^{16} b^{24} - 76908 \, a^{14} b^{26} + 764 \, a^{12} b^{28} + 20908 \, a^{10} b^{30} + 10788 \, a^{8} b^{32} + 2169 \, a^{6} b^{34} + 43 \, a^{4} b^{36} - 29 \, a^{2} b^{38} + b^{40}}\right) \cos\left(d x + c\right)^{2} - 15 \, \sqrt{2} {\left({\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{3} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(49 \, a^{20} b^{2} - 294 \, a^{18} b^{4} - 147 \, a^{16} b^{6} + 1848 \, a^{14} b^{8} + 1778 \, a^{12} b^{10} - 1316 \, a^{10} b^{12} - 1518 \, a^{8} b^{14} + 312 \, a^{6} b^{16} + 349 \, a^{4} b^{18} - 38 \, a^{2} b^{20} + b^{22}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(4 \, {\left(49 \, a^{15} b^{3} - 539 \, a^{13} b^{5} + 2009 \, a^{11} b^{7} - 3003 \, a^{9} b^{9} + 1995 \, a^{7} b^{11} - 553 \, a^{5} b^{13} + 43 \, a^{3} b^{15} - a b^{17}\right)} d^{3} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) + {\left(147 \, a^{22} b^{3} - 931 \, a^{20} b^{5} - 147 \, a^{18} b^{7} + 5691 \, a^{16} b^{9} + 3486 \, a^{14} b^{11} - 5726 \, a^{12} b^{13} - 3238 \, a^{10} b^{15} + 2454 \, a^{8} b^{17} + 735 \, a^{6} b^{19} - 463 \, a^{4} b^{21} + 41 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{27} b^{2} - 147 \, a^{25} b^{4} - 882 \, a^{23} b^{6} + 574 \, a^{21} b^{8} + 6587 \, a^{19} b^{10} + 9415 \, a^{17} b^{12} + 1716 \, a^{15} b^{14} - 6412 \, a^{13} b^{16} - 4585 \, a^{11} b^{18} + 427 \, a^{9} b^{20} + 1246 \, a^{7} b^{22} + 238 \, a^{5} b^{24} - 35 \, a^{3} b^{26} + a b^{28}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{26} b^{3} - 147 \, a^{24} b^{5} - 882 \, a^{22} b^{7} + 574 \, a^{20} b^{9} + 6587 \, a^{18} b^{11} + 9415 \, a^{16} b^{13} + 1716 \, a^{14} b^{15} - 6412 \, a^{12} b^{17} - 4585 \, a^{10} b^{19} + 427 \, a^{8} b^{21} + 1246 \, a^{6} b^{23} + 238 \, a^{4} b^{25} - 35 \, a^{2} b^{27} + b^{29}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) + 15 \, \sqrt{2} {\left({\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{3} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(49 \, a^{20} b^{2} - 294 \, a^{18} b^{4} - 147 \, a^{16} b^{6} + 1848 \, a^{14} b^{8} + 1778 \, a^{12} b^{10} - 1316 \, a^{10} b^{12} - 1518 \, a^{8} b^{14} + 312 \, a^{6} b^{16} + 349 \, a^{4} b^{18} - 38 \, a^{2} b^{20} + b^{22}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(4 \, {\left(49 \, a^{15} b^{3} - 539 \, a^{13} b^{5} + 2009 \, a^{11} b^{7} - 3003 \, a^{9} b^{9} + 1995 \, a^{7} b^{11} - 553 \, a^{5} b^{13} + 43 \, a^{3} b^{15} - a b^{17}\right)} d^{3} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}} \cos\left(d x + c\right) + {\left(147 \, a^{22} b^{3} - 931 \, a^{20} b^{5} - 147 \, a^{18} b^{7} + 5691 \, a^{16} b^{9} + 3486 \, a^{14} b^{11} - 5726 \, a^{12} b^{13} - 3238 \, a^{10} b^{15} + 2454 \, a^{8} b^{17} + 735 \, a^{6} b^{19} - 463 \, a^{4} b^{21} + 41 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14} + {\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} d^{2} \sqrt{\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}}}{49 \, a^{12} b^{2} - 490 \, a^{10} b^{4} + 1519 \, a^{8} b^{6} - 1484 \, a^{6} b^{8} + 511 \, a^{4} b^{10} - 42 \, a^{2} b^{12} + b^{14}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}}{d^{4}}\right)^{\frac{1}{4}} + {\left(49 \, a^{27} b^{2} - 147 \, a^{25} b^{4} - 882 \, a^{23} b^{6} + 574 \, a^{21} b^{8} + 6587 \, a^{19} b^{10} + 9415 \, a^{17} b^{12} + 1716 \, a^{15} b^{14} - 6412 \, a^{13} b^{16} - 4585 \, a^{11} b^{18} + 427 \, a^{9} b^{20} + 1246 \, a^{7} b^{22} + 238 \, a^{5} b^{24} - 35 \, a^{3} b^{26} + a b^{28}\right)} \cos\left(d x + c\right) + {\left(49 \, a^{26} b^{3} - 147 \, a^{24} b^{5} - 882 \, a^{22} b^{7} + 574 \, a^{20} b^{9} + 6587 \, a^{18} b^{11} + 9415 \, a^{16} b^{13} + 1716 \, a^{14} b^{15} - 6412 \, a^{12} b^{17} - 4585 \, a^{10} b^{19} + 427 \, a^{8} b^{21} + 1246 \, a^{6} b^{23} + 238 \, a^{4} b^{25} - 35 \, a^{2} b^{27} + b^{29}\right)} \sin\left(d x + c\right)}{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{14} b^{3} + 21 \, a^{12} b^{5} + 63 \, a^{10} b^{7} + 105 \, a^{8} b^{9} + 105 \, a^{6} b^{11} + 63 \, a^{4} b^{13} + 21 \, a^{2} b^{15} + 3 \, b^{17} + 2 \, {\left(29 \, a^{16} b + 194 \, a^{14} b^{3} + 546 \, a^{12} b^{5} + 826 \, a^{10} b^{7} + 700 \, a^{8} b^{9} + 294 \, a^{6} b^{11} + 14 \, a^{4} b^{13} - 34 \, a^{2} b^{15} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{2} + 16 \, {\left(a^{15} b^{2} + 7 \, a^{13} b^{4} + 21 \, a^{11} b^{6} + 35 \, a^{9} b^{8} + 35 \, a^{7} b^{10} + 21 \, a^{5} b^{12} + 7 \, a^{3} b^{14} + a b^{16}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{14} + 7 \, a^{12} b^{2} + 21 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 35 \, a^{6} b^{8} + 21 \, a^{4} b^{10} + 7 \, a^{2} b^{12} + b^{14}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*d^5*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(3/4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4)*arctan(-((7*a^26 + 35*a^24*b^2 - 14*a^22*b^4 - 526*a^20*b^6 - 1795*a^18*b^8 - 3111*a^16*b^10 - 3060*a^14*b^12 - 1428*a^12*b^14 + 273*a^10*b^16 + 805*a^8*b^18 + 482*a^6*b^20 + 130*a^4*b^22 + 11*a^2*b^24 - b^26)*d^4*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + (7*a^33 + 56*a^31*b^2 + 112*a^29*b^4 - 456*a^27*b^6 - 3380*a^25*b^8 - 10088*a^23*b^10 - 18304*a^21*b^12 - 21736*a^19*b^14 - 16302*a^17*b^16 - 5720*a^15*b^18 + 2288*a^13*b^20 + 4264*a^11*b^22 + 2652*a^9*b^24 + 904*a^7*b^26 + 160*a^5*b^28 + 8*a^3*b^30 - a*b^32)*d^2*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + sqrt(2)*((21*a^14*b - 49*a^12*b^3 - 175*a^10*b^5 - 45*a^8*b^7 + 111*a^6*b^9 + 29*a^4*b^11 - 21*a^2*b^13 + b^15)*d^7*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + 4*(7*a^21*b - 91*a^17*b^5 - 176*a^15*b^7 - 26*a^13*b^9 + 208*a^11*b^11 + 170*a^9*b^13 - 16*a^7*b^15 - 61*a^5*b^17 - 16*a^3*b^19 + a*b^21)*d^5*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(3/4) + sqrt(2)*((3*a^2 - b^2)*d^7*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + 4*(a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt(((49*a^20*b^2 - 294*a^18*b^4 - 147*a^16*b^6 + 1848*a^14*b^8 + 1778*a^12*b^10 - 1316*a^10*b^12 - 1518*a^8*b^14 + 312*a^6*b^16 + 349*a^4*b^18 - 38*a^2*b^20 + b^22)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) + sqrt(2)*(4*(49*a^15*b^3 - 539*a^13*b^5 + 2009*a^11*b^7 - 3003*a^9*b^9 + 1995*a^7*b^11 - 553*a^5*b^13 + 43*a^3*b^15 - a*b^17)*d^3*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) + (147*a^22*b^3 - 931*a^20*b^5 - 147*a^18*b^7 + 5691*a^16*b^9 + 3486*a^14*b^11 - 5726*a^12*b^13 - 3238*a^10*b^15 + 2454*a^8*b^17 + 735*a^6*b^19 - 463*a^4*b^21 + 41*a^2*b^23 - b^25)*d*cos(d*x + c))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(1/4) + (49*a^27*b^2 - 147*a^25*b^4 - 882*a^23*b^6 + 574*a^21*b^8 + 6587*a^19*b^10 + 9415*a^17*b^12 + 1716*a^15*b^14 - 6412*a^13*b^16 - 4585*a^11*b^18 + 427*a^9*b^20 + 1246*a^7*b^22 + 238*a^5*b^24 - 35*a^3*b^26 + a*b^28)*cos(d*x + c) + (49*a^26*b^3 - 147*a^24*b^5 - 882*a^22*b^7 + 574*a^20*b^9 + 6587*a^18*b^11 + 9415*a^16*b^13 + 1716*a^14*b^15 - 6412*a^12*b^17 - 4585*a^10*b^19 + 427*a^8*b^21 + 1246*a^6*b^23 + 238*a^4*b^25 - 35*a^2*b^27 + b^29)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(3/4))/(49*a^38*b^2 + 147*a^36*b^4 - 1029*a^34*b^6 - 5943*a^32*b^8 - 5404*a^30*b^10 + 37996*a^28*b^12 + 154428*a^26*b^14 + 280020*a^24*b^16 + 272350*a^22*b^18 + 92378*a^20*b^20 - 104390*a^18*b^22 - 154050*a^16*b^24 - 76908*a^14*b^26 + 764*a^12*b^28 + 20908*a^10*b^30 + 10788*a^8*b^32 + 2169*a^6*b^34 + 43*a^4*b^36 - 29*a^2*b^38 + b^40))*cos(d*x + c)^2 + 60*sqrt(2)*d^5*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(3/4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4)*arctan(((7*a^26 + 35*a^24*b^2 - 14*a^22*b^4 - 526*a^20*b^6 - 1795*a^18*b^8 - 3111*a^16*b^10 - 3060*a^14*b^12 - 1428*a^12*b^14 + 273*a^10*b^16 + 805*a^8*b^18 + 482*a^6*b^20 + 130*a^4*b^22 + 11*a^2*b^24 - b^26)*d^4*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + (7*a^33 + 56*a^31*b^2 + 112*a^29*b^4 - 456*a^27*b^6 - 3380*a^25*b^8 - 10088*a^23*b^10 - 18304*a^21*b^12 - 21736*a^19*b^14 - 16302*a^17*b^16 - 5720*a^15*b^18 + 2288*a^13*b^20 + 4264*a^11*b^22 + 2652*a^9*b^24 + 904*a^7*b^26 + 160*a^5*b^28 + 8*a^3*b^30 - a*b^32)*d^2*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) - sqrt(2)*((21*a^14*b - 49*a^12*b^3 - 175*a^10*b^5 - 45*a^8*b^7 + 111*a^6*b^9 + 29*a^4*b^11 - 21*a^2*b^13 + b^15)*d^7*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + 4*(7*a^21*b - 91*a^17*b^5 - 176*a^15*b^7 - 26*a^13*b^9 + 208*a^11*b^11 + 170*a^9*b^13 - 16*a^7*b^15 - 61*a^5*b^17 - 16*a^3*b^19 + a*b^21)*d^5*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(3/4) - sqrt(2)*((3*a^2 - b^2)*d^7*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4) + 4*(a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14)/d^4))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt(((49*a^20*b^2 - 294*a^18*b^4 - 147*a^16*b^6 + 1848*a^14*b^8 + 1778*a^12*b^10 - 1316*a^10*b^12 - 1518*a^8*b^14 + 312*a^6*b^16 + 349*a^4*b^18 - 38*a^2*b^20 + b^22)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) - sqrt(2)*(4*(49*a^15*b^3 - 539*a^13*b^5 + 2009*a^11*b^7 - 3003*a^9*b^9 + 1995*a^7*b^11 - 553*a^5*b^13 + 43*a^3*b^15 - a*b^17)*d^3*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) + (147*a^22*b^3 - 931*a^20*b^5 - 147*a^18*b^7 + 5691*a^16*b^9 + 3486*a^14*b^11 - 5726*a^12*b^13 - 3238*a^10*b^15 + 2454*a^8*b^17 + 735*a^6*b^19 - 463*a^4*b^21 + 41*a^2*b^23 - b^25)*d*cos(d*x + c))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(1/4) + (49*a^27*b^2 - 147*a^25*b^4 - 882*a^23*b^6 + 574*a^21*b^8 + 6587*a^19*b^10 + 9415*a^17*b^12 + 1716*a^15*b^14 - 6412*a^13*b^16 - 4585*a^11*b^18 + 427*a^9*b^20 + 1246*a^7*b^22 + 238*a^5*b^24 - 35*a^3*b^26 + a*b^28)*cos(d*x + c) + (49*a^26*b^3 - 147*a^24*b^5 - 882*a^22*b^7 + 574*a^20*b^9 + 6587*a^18*b^11 + 9415*a^16*b^13 + 1716*a^14*b^15 - 6412*a^12*b^17 - 4585*a^10*b^19 + 427*a^8*b^21 + 1246*a^6*b^23 + 238*a^4*b^25 - 35*a^2*b^27 + b^29)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c)))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(3/4))/(49*a^38*b^2 + 147*a^36*b^4 - 1029*a^34*b^6 - 5943*a^32*b^8 - 5404*a^30*b^10 + 37996*a^28*b^12 + 154428*a^26*b^14 + 280020*a^24*b^16 + 272350*a^22*b^18 + 92378*a^20*b^20 - 104390*a^18*b^22 - 154050*a^16*b^24 - 76908*a^14*b^26 + 764*a^12*b^28 + 20908*a^10*b^30 + 10788*a^8*b^32 + 2169*a^6*b^34 + 43*a^4*b^36 - 29*a^2*b^38 + b^40))*cos(d*x + c)^2 - 15*sqrt(2)*((a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^3*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c)^2 - (a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)*d*cos(d*x + c)^2)*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(1/4)*log(((49*a^20*b^2 - 294*a^18*b^4 - 147*a^16*b^6 + 1848*a^14*b^8 + 1778*a^12*b^10 - 1316*a^10*b^12 - 1518*a^8*b^14 + 312*a^6*b^16 + 349*a^4*b^18 - 38*a^2*b^20 + b^22)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) + sqrt(2)*(4*(49*a^15*b^3 - 539*a^13*b^5 + 2009*a^11*b^7 - 3003*a^9*b^9 + 1995*a^7*b^11 - 553*a^5*b^13 + 43*a^3*b^15 - a*b^17)*d^3*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) + (147*a^22*b^3 - 931*a^20*b^5 - 147*a^18*b^7 + 5691*a^16*b^9 + 3486*a^14*b^11 - 5726*a^12*b^13 - 3238*a^10*b^15 + 2454*a^8*b^17 + 735*a^6*b^19 - 463*a^4*b^21 + 41*a^2*b^23 - b^25)*d*cos(d*x + c))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(1/4) + (49*a^27*b^2 - 147*a^25*b^4 - 882*a^23*b^6 + 574*a^21*b^8 + 6587*a^19*b^10 + 9415*a^17*b^12 + 1716*a^15*b^14 - 6412*a^13*b^16 - 4585*a^11*b^18 + 427*a^9*b^20 + 1246*a^7*b^22 + 238*a^5*b^24 - 35*a^3*b^26 + a*b^28)*cos(d*x + c) + (49*a^26*b^3 - 147*a^24*b^5 - 882*a^22*b^7 + 574*a^20*b^9 + 6587*a^18*b^11 + 9415*a^16*b^13 + 1716*a^14*b^15 - 6412*a^12*b^17 - 4585*a^10*b^19 + 427*a^8*b^21 + 1246*a^6*b^23 + 238*a^4*b^25 - 35*a^2*b^27 + b^29)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) + 15*sqrt(2)*((a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^3*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c)^2 - (a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)*d*cos(d*x + c)^2)*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(1/4)*log(((49*a^20*b^2 - 294*a^18*b^4 - 147*a^16*b^6 + 1848*a^14*b^8 + 1778*a^12*b^10 - 1316*a^10*b^12 - 1518*a^8*b^14 + 312*a^6*b^16 + 349*a^4*b^18 - 38*a^2*b^20 + b^22)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) - sqrt(2)*(4*(49*a^15*b^3 - 539*a^13*b^5 + 2009*a^11*b^7 - 3003*a^9*b^9 + 1995*a^7*b^11 - 553*a^5*b^13 + 43*a^3*b^15 - a*b^17)*d^3*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)*cos(d*x + c) + (147*a^22*b^3 - 931*a^20*b^5 - 147*a^18*b^7 + 5691*a^16*b^9 + 3486*a^14*b^11 - 5726*a^12*b^13 - 3238*a^10*b^15 + 2454*a^8*b^17 + 735*a^6*b^19 - 463*a^4*b^21 + 41*a^2*b^23 - b^25)*d*cos(d*x + c))*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14 + (a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*d^2*sqrt((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4))/(49*a^12*b^2 - 490*a^10*b^4 + 1519*a^8*b^6 - 1484*a^6*b^8 + 511*a^4*b^10 - 42*a^2*b^12 + b^14))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)/d^4)^(1/4) + (49*a^27*b^2 - 147*a^25*b^4 - 882*a^23*b^6 + 574*a^21*b^8 + 6587*a^19*b^10 + 9415*a^17*b^12 + 1716*a^15*b^14 - 6412*a^13*b^16 - 4585*a^11*b^18 + 427*a^9*b^20 + 1246*a^7*b^22 + 238*a^5*b^24 - 35*a^3*b^26 + a*b^28)*cos(d*x + c) + (49*a^26*b^3 - 147*a^24*b^5 - 882*a^22*b^7 + 574*a^20*b^9 + 6587*a^18*b^11 + 9415*a^16*b^13 + 1716*a^14*b^15 - 6412*a^12*b^17 - 4585*a^10*b^19 + 427*a^8*b^21 + 1246*a^6*b^23 + 238*a^4*b^25 - 35*a^2*b^27 + b^29)*sin(d*x + c))/((a^2 + b^2)*cos(d*x + c))) - 8*(3*a^14*b^3 + 21*a^12*b^5 + 63*a^10*b^7 + 105*a^8*b^9 + 105*a^6*b^11 + 63*a^4*b^13 + 21*a^2*b^15 + 3*b^17 + 2*(29*a^16*b + 194*a^14*b^3 + 546*a^12*b^5 + 826*a^10*b^7 + 700*a^8*b^9 + 294*a^6*b^11 + 14*a^4*b^13 - 34*a^2*b^15 - 9*b^17)*cos(d*x + c)^2 + 16*(a^15*b^2 + 7*a^13*b^4 + 21*a^11*b^6 + 35*a^9*b^8 + 35*a^7*b^10 + 21*a^5*b^12 + 7*a^3*b^14 + a*b^16)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^14 + 7*a^12*b^2 + 21*a^10*b^4 + 35*a^8*b^6 + 35*a^6*b^8 + 21*a^4*b^10 + 7*a^2*b^12 + b^14)*d*cos(d*x + c)^2)","B",0
528,1,2309,0,0.964076," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{420 \, \sqrt{2} {\left(a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} {\left(a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) \cos\left(d x + c\right)^{3} + 105 \, \sqrt{2} {\left(a b^{4} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)^{3} + b^{4} d \cos\left(d x + c\right)^{3}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 105 \, \sqrt{2} {\left(a b^{4} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)^{3} + b^{4} d \cos\left(d x + c\right)^{3}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(18 \, a b^{2} \cos\left(d x + c\right) + 8 \, {\left(6 \, a^{3} - 11 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(15 \, b^{3} + 2 \, {\left(12 \, a^{2} b - 25 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{420 \, b^{4} d \cos\left(d x + c\right)^{3}}"," ",0,"-1/420*(420*sqrt(2)*(a^2*b^4 + b^6)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2)*cos(d*x + c)^3 + 420*sqrt(2)*(a^2*b^4 + b^6)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2)*cos(d*x + c)^3 + 105*sqrt(2)*(a*b^4*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c)^3 + b^4*d*cos(d*x + c)^3)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - 105*sqrt(2)*(a*b^4*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c)^3 + b^4*d*cos(d*x + c)^3)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + 8*(18*a*b^2*cos(d*x + c) + 8*(6*a^3 - 11*a*b^2)*cos(d*x + c)^3 - (15*b^3 + 2*(12*a^2*b - 25*b^3)*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(b^4*d*cos(d*x + c)^3)","B",0
529,1,1886,0,1.043803," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} {\left(a^{2} b^{3} + b^{5}\right)} d^{5} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} {\left(a^{2} b^{3} + b^{5}\right)} d^{5} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) \cos\left(d x + c\right)^{2} + 15 \, \sqrt{2} {\left(a b^{3} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)^{2} - b^{3} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left(a b^{3} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right)^{2} - b^{3} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(4 \, a^{2} - 9 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, b^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, b^{3} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*(a^2*b^3 + b^5)*d^5*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) - (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2)*cos(d*x + c)^2 + 60*sqrt(2)*(a^2*b^3 + b^5)*d^5*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2)*cos(d*x + c)^2 + 15*sqrt(2)*(a*b^3*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c)^2 - b^3*d*cos(d*x + c)^2)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*(a*b^3*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c)^2 - b^3*d*cos(d*x + c)^2)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c)) + 8*(4*a*b*cos(d*x + c)*sin(d*x + c) - 2*(4*a^2 - 9*b^2)*cos(d*x + c)^2 - 3*b^2)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(b^3*d*cos(d*x + c)^2)","B",0
530,1,2245,0,0.781078," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left(a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} {\left(a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left(a b^{2} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + b^{2} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left(a b^{2} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + b^{2} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(2 \, a \cos\left(d x + c\right) - b \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, b^{2} d \cos\left(d x + c\right)}"," ",0,"1/12*(12*sqrt(2)*(a^2*b^2 + b^4)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2)*cos(d*x + c) + 12*sqrt(2)*(a^2*b^2 + b^4)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2)*cos(d*x + c) + 3*sqrt(2)*(a*b^2*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + b^2*d*cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(a*b^2*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + b^2*d*cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - 8*(2*a*cos(d*x + c) - b*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(b^2*d*cos(d*x + c))","B",0
531,1,1774,0,1.000492," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) + \sqrt{2} {\left(a b d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - b d\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(a b d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - b d\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, b d}"," ",0,"1/4*(4*sqrt(2)*(a^2*b + b^3)*d^5*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) - (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) + 4*sqrt(2)*(a^2*b + b^3)*d^5*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) + sqrt(2)*(a*b*d^3*sqrt(1/((a^2 + b^2)*d^4)) - b*d)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(a*b*d^3*sqrt(1/((a^2 + b^2)*d^4)) - b*d)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c)) + 8*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(b*d)","B",0
532,1,2122,0,1.002887," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) - \sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) - \frac{1}{4} \, \sqrt{2} {\left(a d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + 1\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \frac{1}{4} \, \sqrt{2} {\left(a d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + 1\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)"," ",0,"-sqrt(2)*(a^2 + b^2)*d^4*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) - sqrt(2)*(a^2 + b^2)*d^4*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) - 1/4*sqrt(2)*(a*d^2*sqrt(1/((a^2 + b^2)*d^4)) + 1)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + 1/4*sqrt(2)*(a*d^2*sqrt(1/((a^2 + b^2)*d^4)) + 1)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))","B",0
533,1,1725,0,0.533079," ","integrate(1/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) - \sqrt{2} {\left(a^{2} + b^{2}\right)} d^{4} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) - \frac{1}{4} \, \sqrt{2} {\left(a d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - 1\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \frac{1}{4} \, \sqrt{2} {\left(a d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - 1\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)"," ",0,"-sqrt(2)*(a^2 + b^2)*d^4*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) - (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) - sqrt(2)*(a^2 + b^2)*d^4*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) - 1/4*sqrt(2)*(a*d^2*sqrt(1/((a^2 + b^2)*d^4)) - 1)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c)) + 1/4*sqrt(2)*(a*d^2*sqrt(1/((a^2 + b^2)*d^4)) - 1)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))","B",0
534,1,4447,0,3.059834," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + \sqrt{2} {\left(a^{2} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a d\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(a^{2} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a d\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 2 \, \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, a d}, \frac{4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + \sqrt{2} {\left(a^{2} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a d\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(a^{2} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a d\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, a d}\right]"," ",0,"[1/4*(4*sqrt(2)*(a^3 + a*b^2)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + 4*sqrt(2)*(a^3 + a*b^2)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + sqrt(2)*(a^2*d^3*sqrt(1/((a^2 + b^2)*d^4)) + a*d)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(a^2*d^3*sqrt(1/((a^2 + b^2)*d^4)) + a*d)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + 2*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/(a*d), 1/4*(4*sqrt(2)*(a^3 + a*b^2)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + 4*sqrt(2)*(a^3 + a*b^2)*d^5*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + sqrt(2)*(a^2*d^3*sqrt(1/((a^2 + b^2)*d^4)) + a*d)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(a^2*d^3*sqrt(1/((a^2 + b^2)*d^4)) + a*d)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + 8*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/(a*d)]","B",0
535,1,4050,0,2.497671," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{5}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{5}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) + 4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + {\left(b \cos\left(d x + c\right)^{2} - b\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}, \frac{4 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{5}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{5}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{7} \sqrt{-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} - \sqrt{2} {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{7} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{5}{4}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{b^{2}}\right) + 4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{3} d^{3} \cos\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + a^{2} + b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*((a^4 + a^2*b^2)*d^5*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d^5)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) - (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) + 4*sqrt(2)*((a^4 + a^2*b^2)*d^5*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d^5)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) + 4*a*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*(a^2*d*cos(d*x + c)^2 - a^2*d - (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(a^2*d*cos(d*x + c)^2 - a^2*d - (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c)) + (b*cos(d*x + c)^2 - b)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 + 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)))/(a^2*d*cos(d*x + c)^2 - a^2*d), 1/4*(4*sqrt(2)*((a^4 + a^2*b^2)*d^5*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d^5)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) - (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) + 4*sqrt(2)*((a^4 + a^2*b^2)*d^5*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d^5)*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan((sqrt(2)*(a^4 + 2*a^2*b^2 + b^4)*d^7*sqrt(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) - sqrt(2)*(a^4*b + 2*a^2*b^3 + b^5)*d^7*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(5/4) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/b^2) + 4*a*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*(a^2*d*cos(d*x + c)^2 - a^2*d - (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log((sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) + (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*b^2*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(a^2*d*cos(d*x + c)^2 - a^2*d - (a^3*d^3*cos(d*x + c)^2 - a^3*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(-(sqrt(2)*b^3*d*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) + a^2 + b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*cos(d*x + c) - (a^2*b^2 + b^4)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - a*b^2*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c)) - 4*(b*cos(d*x + c)^2 - b)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a))/(a^2*d*cos(d*x + c)^2 - a^2*d)]","B",0
536,1,4908,0,3.400317," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{16 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{5}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + 16 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{5}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d + {\left(a^{4} d^{3} \cos\left(d x + c\right)^{2} - a^{4} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, \sqrt{2} {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d + {\left(a^{4} d^{3} \cos\left(d x + c\right)^{2} - a^{4} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + {\left({\left(8 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 3 \, b^{2}\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) - 4 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 3 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}, -\frac{4 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{5}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{5}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{7} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{5} \sqrt{\frac{b^{2}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{3}{4}}}{b^{2}}\right) + \sqrt{2} {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d + {\left(a^{4} d^{3} \cos\left(d x + c\right)^{2} - a^{4} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d + {\left(a^{4} d^{3} \cos\left(d x + c\right)^{2} - a^{4} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{2} + b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} \cos\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{{\left(a^{3} + a b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}} - a^{2} - b^{2}}{b^{2}}} \left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{4}}\right)^{\frac{1}{4}} + a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + {\left({\left(8 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 3 \, b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 3 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}\right]"," ",0,"[-1/16*(16*sqrt(2)*((a^5 + a^3*b^2)*d^5*cos(d*x + c)^2 - (a^5 + a^3*b^2)*d^5)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + 16*sqrt(2)*((a^5 + a^3*b^2)*d^5*cos(d*x + c)^2 - (a^5 + a^3*b^2)*d^5)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + 4*sqrt(2)*(a^3*d*cos(d*x + c)^2 - a^3*d + (a^4*d^3*cos(d*x + c)^2 - a^4*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - 4*sqrt(2)*(a^3*d*cos(d*x + c)^2 - a^3*d + (a^4*d^3*cos(d*x + c)^2 - a^4*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + ((8*a^2 - 3*b^2)*cos(d*x + c)^2 - 8*a^2 + 3*b^2)*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) - 4*(2*a^2*cos(d*x + c)^2 - 3*a*b*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(a^3*d*cos(d*x + c)^2 - a^3*d), -1/4*(4*sqrt(2)*((a^5 + a^3*b^2)*d^5*cos(d*x + c)^2 - (a^5 + a^3*b^2)*d^5)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(-((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + 4*sqrt(2)*((a^5 + a^3*b^2)*d^5*cos(d*x + c)^2 - (a^5 + a^3*b^2)*d^5)*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*(1/((a^2 + b^2)*d^4))^(3/4)*arctan(((a^4 + 2*a^2*b^2 + b^4)*d^4*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^3 + a*b^2)*d^2*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4) - sqrt(2)*((a^5 + 2*a^3*b^2 + a*b^4)*d^7*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4))*sqrt(1/((a^2 + b^2)*d^4)) + (a^4 + 2*a^2*b^2 + b^4)*d^5*sqrt(b^2/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(3/4))/b^2) + sqrt(2)*(a^3*d*cos(d*x + c)^2 - a^3*d + (a^4*d^3*cos(d*x + c)^2 - a^4*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(a^3*d*cos(d*x + c)^2 - a^3*d + (a^4*d^3*cos(d*x + c)^2 - a^4*d^3)*sqrt(1/((a^2 + b^2)*d^4)))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4)*log(((a^2 + b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) - sqrt(2)*((a^2 + b^2)*d^3*sqrt(1/((a^2 + b^2)*d^4))*cos(d*x + c) + a*d*cos(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*sqrt(-((a^3 + a*b^2)*d^2*sqrt(1/((a^2 + b^2)*d^4)) - a^2 - b^2)/b^2)*(1/((a^2 + b^2)*d^4))^(1/4) + a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + ((8*a^2 - 3*b^2)*cos(d*x + c)^2 - 8*a^2 + 3*b^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) - (2*a^2*cos(d*x + c)^2 - 3*a*b*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(a^3*d*cos(d*x + c)^2 - a^3*d)]","B",0
537,1,5852,0,2.772067," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} {\left({\left(a^{10} b^{4} + 3 \, a^{8} b^{6} + 2 \, a^{6} b^{8} - 2 \, a^{4} b^{10} - 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b^{5} + 4 \, a^{7} b^{7} + 6 \, a^{5} b^{9} + 4 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{8} b^{6} + 4 \, a^{6} b^{8} + 6 \, a^{4} b^{10} + 4 \, a^{2} b^{12} + b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 20 \, \sqrt{2} {\left({\left(a^{10} b^{4} + 3 \, a^{8} b^{6} + 2 \, a^{6} b^{8} - 2 \, a^{4} b^{10} - 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b^{5} + 4 \, a^{7} b^{7} + 6 \, a^{5} b^{9} + 4 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{8} b^{6} + 4 \, a^{6} b^{8} + 6 \, a^{4} b^{10} + 4 \, a^{2} b^{12} + b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 5 \, \sqrt{2} {\left({\left(a^{4} b^{4} - b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(a^{7} b^{4} - 3 \, a^{5} b^{6} - a^{3} b^{8} + 3 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 5 \, \sqrt{2} {\left({\left(a^{4} b^{4} - b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(a^{7} b^{4} - 3 \, a^{5} b^{6} - a^{3} b^{8} + 3 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(a^{2} b^{4} + b^{6} + {\left(16 \, a^{6} - 5 \, a^{2} b^{4} + 6 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(6 \, a^{4} b^{2} - a^{2} b^{4} - 7 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(24 \, a^{5} b + 10 \, a^{3} b^{3} - 9 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{20 \, {\left({\left(a^{4} b^{4} - b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/20*(20*sqrt(2)*((a^10*b^4 + 3*a^8*b^6 + 2*a^6*b^8 - 2*a^4*b^10 - 3*a^2*b^12 - b^14)*d^5*cos(d*x + c)^4 + 2*(a^9*b^5 + 4*a^7*b^7 + 6*a^5*b^9 + 4*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)^3*sin(d*x + c) + (a^8*b^6 + 4*a^6*b^8 + 6*a^4*b^10 + 4*a^2*b^12 + b^14)*d^5*cos(d*x + c)^2)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 20*sqrt(2)*((a^10*b^4 + 3*a^8*b^6 + 2*a^6*b^8 - 2*a^4*b^10 - 3*a^2*b^12 - b^14)*d^5*cos(d*x + c)^4 + 2*(a^9*b^5 + 4*a^7*b^7 + 6*a^5*b^9 + 4*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)^3*sin(d*x + c) + (a^8*b^6 + 4*a^6*b^8 + 6*a^4*b^10 + 4*a^2*b^12 + b^14)*d^5*cos(d*x + c)^2)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 5*sqrt(2)*((a^4*b^4 - b^8)*d*cos(d*x + c)^4 + 2*(a^3*b^5 + a*b^7)*d*cos(d*x + c)^3*sin(d*x + c) + (a^2*b^6 + b^8)*d*cos(d*x + c)^2 + ((a^7*b^4 - 3*a^5*b^6 - a^3*b^8 + 3*a*b^10)*d^3*cos(d*x + c)^4 + 2*(a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9)*d^3*cos(d*x + c)^3*sin(d*x + c) + (a^5*b^6 - 2*a^3*b^8 - 3*a*b^10)*d^3*cos(d*x + c)^2)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - 5*sqrt(2)*((a^4*b^4 - b^8)*d*cos(d*x + c)^4 + 2*(a^3*b^5 + a*b^7)*d*cos(d*x + c)^3*sin(d*x + c) + (a^2*b^6 + b^8)*d*cos(d*x + c)^2 + ((a^7*b^4 - 3*a^5*b^6 - a^3*b^8 + 3*a*b^10)*d^3*cos(d*x + c)^4 + 2*(a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9)*d^3*cos(d*x + c)^3*sin(d*x + c) + (a^5*b^6 - 2*a^3*b^8 - 3*a*b^10)*d^3*cos(d*x + c)^2)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - 8*(a^2*b^4 + b^6 + (16*a^6 - 5*a^2*b^4 + 6*b^6)*cos(d*x + c)^4 + (6*a^4*b^2 - a^2*b^4 - 7*b^6)*cos(d*x + c)^2 + ((24*a^5*b + 10*a^3*b^3 - 9*a*b^5)*cos(d*x + c)^3 - (a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4*b^4 - b^8)*d*cos(d*x + c)^4 + 2*(a^3*b^5 + a*b^7)*d*cos(d*x + c)^3*sin(d*x + c) + (a^2*b^6 + b^8)*d*cos(d*x + c)^2)","B",0
538,1,5793,0,1.397741," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(a^{10} b^{3} + 3 \, a^{8} b^{5} + 2 \, a^{6} b^{7} - 2 \, a^{4} b^{9} - 3 \, a^{2} b^{11} - b^{13}\right)} d^{5} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{9} b^{4} + 4 \, a^{7} b^{6} + 6 \, a^{5} b^{8} + 4 \, a^{3} b^{10} + a b^{12}\right)} d^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{8} b^{5} + 4 \, a^{6} b^{7} + 6 \, a^{4} b^{9} + 4 \, a^{2} b^{11} + b^{13}\right)} d^{5} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 12 \, \sqrt{2} {\left({\left(a^{10} b^{3} + 3 \, a^{8} b^{5} + 2 \, a^{6} b^{7} - 2 \, a^{4} b^{9} - 3 \, a^{2} b^{11} - b^{13}\right)} d^{5} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{9} b^{4} + 4 \, a^{7} b^{6} + 6 \, a^{5} b^{8} + 4 \, a^{3} b^{10} + a b^{12}\right)} d^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{8} b^{5} + 4 \, a^{6} b^{7} + 6 \, a^{4} b^{9} + 4 \, a^{2} b^{11} + b^{13}\right)} d^{5} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 3 \, \sqrt{2} {\left({\left(a^{4} b^{3} - b^{7}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right) - {\left({\left(a^{7} b^{3} - 3 \, a^{5} b^{5} - a^{3} b^{7} + 3 \, a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} - 3 \, a b^{9}\right)} d^{3} \cos\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{4} b^{3} - b^{7}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right) - {\left({\left(a^{7} b^{3} - 3 \, a^{5} b^{5} - a^{3} b^{7} + 3 \, a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} - 3 \, a b^{9}\right)} d^{3} \cos\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left({\left(8 \, a^{5} + 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5} - {\left(12 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{4} b^{3} - b^{7}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(12*sqrt(2)*((a^10*b^3 + 3*a^8*b^5 + 2*a^6*b^7 - 2*a^4*b^9 - 3*a^2*b^11 - b^13)*d^5*cos(d*x + c)^3 + 2*(a^9*b^4 + 4*a^7*b^6 + 6*a^5*b^8 + 4*a^3*b^10 + a*b^12)*d^5*cos(d*x + c)^2*sin(d*x + c) + (a^8*b^5 + 4*a^6*b^7 + 6*a^4*b^9 + 4*a^2*b^11 + b^13)*d^5*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 12*sqrt(2)*((a^10*b^3 + 3*a^8*b^5 + 2*a^6*b^7 - 2*a^4*b^9 - 3*a^2*b^11 - b^13)*d^5*cos(d*x + c)^3 + 2*(a^9*b^4 + 4*a^7*b^6 + 6*a^5*b^8 + 4*a^3*b^10 + a*b^12)*d^5*cos(d*x + c)^2*sin(d*x + c) + (a^8*b^5 + 4*a^6*b^7 + 6*a^4*b^9 + 4*a^2*b^11 + b^13)*d^5*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 3*sqrt(2)*((a^4*b^3 - b^7)*d*cos(d*x + c)^3 + 2*(a^3*b^4 + a*b^6)*d*cos(d*x + c)^2*sin(d*x + c) + (a^2*b^5 + b^7)*d*cos(d*x + c) - ((a^7*b^3 - 3*a^5*b^5 - a^3*b^7 + 3*a*b^9)*d^3*cos(d*x + c)^3 + 2*(a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8)*d^3*cos(d*x + c)^2*sin(d*x + c) + (a^5*b^5 - 2*a^3*b^7 - 3*a*b^9)*d^3*cos(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^4*b^3 - b^7)*d*cos(d*x + c)^3 + 2*(a^3*b^4 + a*b^6)*d*cos(d*x + c)^2*sin(d*x + c) + (a^2*b^5 + b^7)*d*cos(d*x + c) - ((a^7*b^3 - 3*a^5*b^5 - a^3*b^7 + 3*a*b^9)*d^3*cos(d*x + c)^3 + 2*(a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8)*d^3*cos(d*x + c)^2*sin(d*x + c) + (a^5*b^5 - 2*a^3*b^7 - 3*a*b^9)*d^3*cos(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - 8*((8*a^5 + 2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3 + 3*(a^3*b^2 + a*b^4)*cos(d*x + c) - (a^2*b^3 + b^5 - (12*a^4*b + 10*a^2*b^3 + b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4*b^3 - b^7)*d*cos(d*x + c)^3 + 2*(a^3*b^4 + a*b^6)*d*cos(d*x + c)^2*sin(d*x + c) + (a^2*b^5 + b^7)*d*cos(d*x + c))","B",0
539,1,5709,0,1.892726," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 2 \, a^{6} b^{6} - 2 \, a^{4} b^{8} - 3 \, a^{2} b^{10} - b^{12}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{3} + 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 4 \, a^{3} b^{9} + a b^{11}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 2 \, a^{6} b^{6} - 2 \, a^{4} b^{8} - 3 \, a^{2} b^{10} - b^{12}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{3} + 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 4 \, a^{3} b^{9} + a b^{11}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{4} b^{2} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{4} + b^{6}\right)} d + {\left({\left(a^{7} b^{2} - 3 \, a^{5} b^{4} - a^{3} b^{6} + 3 \, a b^{8}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b^{3} - 2 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{4} b^{2} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{4} + b^{6}\right)} d + {\left({\left(a^{7} b^{2} - 3 \, a^{5} b^{4} - a^{3} b^{6} + 3 \, a b^{8}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b^{3} - 2 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{2} b^{2} + b^{4} + {\left(2 \, a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{4} b^{2} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"1/4*(4*sqrt(2)*((a^10*b^2 + 3*a^8*b^4 + 2*a^6*b^6 - 2*a^4*b^8 - 3*a^2*b^10 - b^12)*d^5*cos(d*x + c)^2 + 2*(a^9*b^3 + 4*a^7*b^5 + 6*a^5*b^7 + 4*a^3*b^9 + a*b^11)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^10*b^2 + 3*a^8*b^4 + 2*a^6*b^6 - 2*a^4*b^8 - 3*a^2*b^10 - b^12)*d^5*cos(d*x + c)^2 + 2*(a^9*b^3 + 4*a^7*b^5 + 6*a^5*b^7 + 4*a^3*b^9 + a*b^11)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^4*b^2 - b^6)*d*cos(d*x + c)^2 + 2*(a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^4 + b^6)*d + ((a^7*b^2 - 3*a^5*b^4 - a^3*b^6 + 3*a*b^8)*d^3*cos(d*x + c)^2 + 2*(a^6*b^3 - 2*a^4*b^5 - 3*a^2*b^7)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^4 - 2*a^3*b^6 - 3*a*b^8)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^4*b^2 - b^6)*d*cos(d*x + c)^2 + 2*(a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^4 + b^6)*d + ((a^7*b^2 - 3*a^5*b^4 - a^3*b^6 + 3*a*b^8)*d^3*cos(d*x + c)^2 + 2*(a^6*b^3 - 2*a^4*b^5 - 3*a^2*b^7)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^4 - 2*a^3*b^6 - 3*a*b^8)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) + 8*(a^2*b^2 + b^4 + (2*a^4 - b^4)*cos(d*x + c)^2 + (3*a^3*b + 2*a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4*b^2 - b^6)*d*cos(d*x + c)^2 + 2*(a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^4 + b^6)*d)","B",0
540,1,5654,0,1.823354," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d - {\left({\left(a^{7} b - 3 \, a^{5} b^{3} - a^{3} b^{5} + 3 \, a b^{7}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} - 3 \, a^{2} b^{6}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} - 3 \, a b^{7}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d - {\left({\left(a^{7} b - 3 \, a^{5} b^{3} - a^{3} b^{5} + 3 \, a b^{7}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} - 3 \, a^{2} b^{6}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} - 3 \, a b^{7}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{4} b - b^{5}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d\right)}}"," ",0,"-1/4*(4*sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^5*cos(d*x + c)^2 + 2*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^5*cos(d*x + c)^2 + 2*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^4*b - b^5)*d*cos(d*x + c)^2 + 2*(a^3*b^2 + a*b^4)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^3 + b^5)*d - ((a^7*b - 3*a^5*b^3 - a^3*b^5 + 3*a*b^7)*d^3*cos(d*x + c)^2 + 2*(a^6*b^2 - 2*a^4*b^4 - 3*a^2*b^6)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^3 - 2*a^3*b^5 - 3*a*b^7)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^4*b - b^5)*d*cos(d*x + c)^2 + 2*(a^3*b^2 + a*b^4)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^3 + b^5)*d - ((a^7*b - 3*a^5*b^3 - a^3*b^5 + 3*a*b^7)*d^3*cos(d*x + c)^2 + 2*(a^6*b^2 - 2*a^4*b^4 - 3*a^2*b^6)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^3 - 2*a^3*b^5 - 3*a*b^7)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) + 8*(a^3*cos(d*x + c)^2 + a^2*b*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4*b - b^5)*d*cos(d*x + c)^2 + 2*(a^3*b^2 + a*b^4)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^3 + b^5)*d)","B",0
541,1,5638,0,2.391358," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{4} - b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d + {\left({\left(a^{7} - 3 \, a^{5} b^{2} - a^{3} b^{4} + 3 \, a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{4} - b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d + {\left({\left(a^{7} - 3 \, a^{5} b^{2} - a^{3} b^{4} + 3 \, a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{4} - b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d\right)}}"," ",0,"-1/4*(4*sqrt(2)*((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d^5*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d^5*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^4 - b^4)*d*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4)*d + ((a^7 - 3*a^5*b^2 - a^3*b^4 + 3*a*b^6)*d^3*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 - 3*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 - 2*a^3*b^4 - 3*a*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^4 - b^4)*d*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4)*d + ((a^7 - 3*a^5*b^2 - a^3*b^4 + 3*a*b^6)*d^3*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 - 3*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 - 2*a^3*b^4 - 3*a*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - 8*(a^2*cos(d*x + c)^2 + a*b*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4 - b^4)*d*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4)*d)","B",0
542,1,5624,0,1.767046," ","integrate(1/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{4} - b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d - {\left({\left(a^{7} - 3 \, a^{5} b^{2} - a^{3} b^{4} + 3 \, a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{4} - b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d - {\left({\left(a^{7} - 3 \, a^{5} b^{2} - a^{3} b^{4} + 3 \, a b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(a b \cos\left(d x + c\right)^{2} + b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{4} - b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d\right)}}"," ",0,"1/4*(4*sqrt(2)*((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d^5*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d^5*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^4 - b^4)*d*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4)*d - ((a^7 - 3*a^5*b^2 - a^3*b^4 + 3*a*b^6)*d^3*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 - 3*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 - 2*a^3*b^4 - 3*a*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^4 - b^4)*d*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4)*d - ((a^7 - 3*a^5*b^2 - a^3*b^4 + 3*a*b^6)*d^3*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 - 3*a^2*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 - 2*a^3*b^4 - 3*a*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - 8*(a*b*cos(d*x + c)^2 + b^2*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^4 - b^4)*d*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4)*d)","B",0
543,1,11665,0,5.170666," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(a^{12} + 3 \, a^{10} b^{2} + 2 \, a^{8} b^{4} - 2 \, a^{6} b^{6} - 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{12} + 3 \, a^{10} b^{2} + 2 \, a^{8} b^{4} - 2 \, a^{6} b^{6} - 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{6} - a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + a^{2} b^{4}\right)} d + {\left({\left(a^{9} - 3 \, a^{7} b^{2} - a^{5} b^{4} + 3 \, a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} - 3 \, a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{6} - a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + a^{2} b^{4}\right)} d + {\left({\left(a^{9} - 3 \, a^{7} b^{2} - a^{5} b^{4} + 3 \, a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} - 3 \, a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 2 \, {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) + 8 \, {\left(a^{2} b^{2} \cos\left(d x + c\right)^{2} + a b^{3} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} - a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + a^{2} b^{4}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left({\left(a^{12} + 3 \, a^{10} b^{2} + 2 \, a^{8} b^{4} - 2 \, a^{6} b^{6} - 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{12} + 3 \, a^{10} b^{2} + 2 \, a^{8} b^{4} - 2 \, a^{6} b^{6} - 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d^{5}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{6} - a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + a^{2} b^{4}\right)} d + {\left({\left(a^{9} - 3 \, a^{7} b^{2} - a^{5} b^{4} + 3 \, a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} - 3 \, a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{6} - a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + a^{2} b^{4}\right)} d + {\left({\left(a^{9} - 3 \, a^{7} b^{2} - a^{5} b^{4} + 3 \, a^{3} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} - 3 \, a^{4} b^{5}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) + 8 \, {\left(a^{2} b^{2} \cos\left(d x + c\right)^{2} + a b^{3} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} - a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + a^{2} b^{4}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*((a^12 + 3*a^10*b^2 + 2*a^8*b^4 - 2*a^6*b^6 - 3*a^4*b^8 - a^2*b^10)*d^5*cos(d*x + c)^2 + 2*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^12 + 3*a^10*b^2 + 2*a^8*b^4 - 2*a^6*b^6 - 3*a^4*b^8 - a^2*b^10)*d^5*cos(d*x + c)^2 + 2*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^6 - a^2*b^4)*d*cos(d*x + c)^2 + 2*(a^5*b + a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + a^2*b^4)*d + ((a^9 - 3*a^7*b^2 - a^5*b^4 + 3*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(a^8*b - 2*a^6*b^3 - 3*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^2 - 2*a^5*b^4 - 3*a^3*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^6 - a^2*b^4)*d*cos(d*x + c)^2 + 2*(a^5*b + a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + a^2*b^4)*d + ((a^9 - 3*a^7*b^2 - a^5*b^4 + 3*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(a^8*b - 2*a^6*b^3 - 3*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^2 - 2*a^5*b^4 - 3*a^3*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) + 2*(a^2*b^2 + b^4 + (a^4 - b^4)*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) + 8*(a^2*b^2*cos(d*x + c)^2 + a*b^3*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6 - a^2*b^4)*d*cos(d*x + c)^2 + 2*(a^5*b + a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + a^2*b^4)*d), 1/4*(4*sqrt(2)*((a^12 + 3*a^10*b^2 + 2*a^8*b^4 - 2*a^6*b^6 - 3*a^4*b^8 - a^2*b^10)*d^5*cos(d*x + c)^2 + 2*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^12 + 3*a^10*b^2 + 2*a^8*b^4 - 2*a^6*b^6 - 3*a^4*b^8 - a^2*b^10)*d^5*cos(d*x + c)^2 + 2*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*d^5*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*d^5)*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^6 - a^2*b^4)*d*cos(d*x + c)^2 + 2*(a^5*b + a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + a^2*b^4)*d + ((a^9 - 3*a^7*b^2 - a^5*b^4 + 3*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(a^8*b - 2*a^6*b^3 - 3*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^2 - 2*a^5*b^4 - 3*a^3*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^6 - a^2*b^4)*d*cos(d*x + c)^2 + 2*(a^5*b + a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + a^2*b^4)*d + ((a^9 - 3*a^7*b^2 - a^5*b^4 + 3*a^3*b^6)*d^3*cos(d*x + c)^2 + 2*(a^8*b - 2*a^6*b^3 - 3*a^4*b^5)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^2 - 2*a^5*b^4 - 3*a^3*b^6)*d^3)*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) + 8*(a^2*b^2 + b^4 + (a^4 - b^4)*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) + 8*(a^2*b^2*cos(d*x + c)^2 + a*b^3*cos(d*x + c)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^6 - a^2*b^4)*d*cos(d*x + c)^2 + 2*(a^5*b + a^3*b^3)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + a^2*b^4)*d)]","B",0
544,1,12983,0,2.442347," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left({\left(a^{13} + 3 \, a^{11} b^{2} + 2 \, a^{9} b^{4} - 2 \, a^{7} b^{6} - 3 \, a^{5} b^{8} - a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{13} + 2 \, a^{11} b^{2} - 2 \, a^{9} b^{4} - 8 \, a^{7} b^{6} - 7 \, a^{5} b^{8} - 2 \, a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{11} b^{2} + 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} + 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{13} + 3 \, a^{11} b^{2} + 2 \, a^{9} b^{4} - 2 \, a^{7} b^{6} - 3 \, a^{5} b^{8} - a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{13} + 2 \, a^{11} b^{2} - 2 \, a^{9} b^{4} - 8 \, a^{7} b^{6} - 7 \, a^{5} b^{8} - 2 \, a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{11} b^{2} + 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} + 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{7} - a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{10} - 3 \, a^{8} b^{2} - a^{6} b^{4} + 3 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{10} - 4 \, a^{8} b^{2} + a^{6} b^{4} + 6 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{8} b^{2} - 2 \, a^{6} b^{4} - 3 \, a^{4} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{7} - a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{10} - 3 \, a^{8} b^{2} - a^{6} b^{4} + 3 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{10} - 4 \, a^{8} b^{2} + a^{6} b^{4} + 6 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{8} b^{2} - 2 \, a^{6} b^{4} - 3 \, a^{4} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, {\left(a^{2} b^{3} + b^{5} - {\left(a^{4} b - b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{4} b - a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) + 4 \, {\left(2 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{5} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{7} - a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}, -\frac{4 \, \sqrt{2} {\left({\left(a^{13} + 3 \, a^{11} b^{2} + 2 \, a^{9} b^{4} - 2 \, a^{7} b^{6} - 3 \, a^{5} b^{8} - a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{13} + 2 \, a^{11} b^{2} - 2 \, a^{9} b^{4} - 8 \, a^{7} b^{6} - 7 \, a^{5} b^{8} - 2 \, a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{11} b^{2} + 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} + 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{13} + 3 \, a^{11} b^{2} + 2 \, a^{9} b^{4} - 2 \, a^{7} b^{6} - 3 \, a^{5} b^{8} - a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{13} + 2 \, a^{11} b^{2} - 2 \, a^{9} b^{4} - 8 \, a^{7} b^{6} - 7 \, a^{5} b^{8} - 2 \, a^{3} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{11} b^{2} + 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} + 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{13} + 6 \, a^{11} b^{2} + 15 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 15 \, a^{5} b^{8} + 6 \, a^{3} b^{10} + a b^{12}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(3 \, a^{15} b + 17 \, a^{13} b^{3} + 39 \, a^{11} b^{5} + 45 \, a^{9} b^{7} + 25 \, a^{7} b^{9} + 3 \, a^{5} b^{11} - 3 \, a^{3} b^{13} - a b^{15}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{12} b + 14 \, a^{10} b^{3} + 25 \, a^{8} b^{5} + 20 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 2 \, a^{2} b^{11} - b^{13}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{7} - a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{10} - 3 \, a^{8} b^{2} - a^{6} b^{4} + 3 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{10} - 4 \, a^{8} b^{2} + a^{6} b^{4} + 6 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{8} b^{2} - 2 \, a^{6} b^{4} - 3 \, a^{4} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{7} - a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{10} - 3 \, a^{8} b^{2} - a^{6} b^{4} + 3 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{10} - 4 \, a^{8} b^{2} + a^{6} b^{4} + 6 \, a^{4} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{8} b^{2} - 2 \, a^{6} b^{4} - 3 \, a^{4} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{9} b - 2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{8} b^{3} + 12 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(9 \, a^{5} b^{3} - 6 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} b^{2} - 6 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 12 \, {\left(a^{2} b^{3} + b^{5} - {\left(a^{4} b - b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{4} b - a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) + 4 \, {\left(2 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{5} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{7} - a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{6} b + a^{4} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*sqrt(2)*((a^13 + 3*a^11*b^2 + 2*a^9*b^4 - 2*a^7*b^6 - 3*a^5*b^8 - a^3*b^10)*d^5*cos(d*x + c)^4 - (a^13 + 2*a^11*b^2 - 2*a^9*b^4 - 8*a^7*b^6 - 7*a^5*b^8 - 2*a^3*b^10)*d^5*cos(d*x + c)^2 - (a^11*b^2 + 4*a^9*b^4 + 6*a^7*b^6 + 4*a^5*b^8 + a^3*b^10)*d^5 + 2*((a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c)^3 - (a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^13 + 3*a^11*b^2 + 2*a^9*b^4 - 2*a^7*b^6 - 3*a^5*b^8 - a^3*b^10)*d^5*cos(d*x + c)^4 - (a^13 + 2*a^11*b^2 - 2*a^9*b^4 - 8*a^7*b^6 - 7*a^5*b^8 - 2*a^3*b^10)*d^5*cos(d*x + c)^2 - (a^11*b^2 + 4*a^9*b^4 + 6*a^7*b^6 + 4*a^5*b^8 + a^3*b^10)*d^5 + 2*((a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c)^3 - (a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^7 - a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - a^5*b^2 - 2*a^3*b^4)*d*cos(d*x + c)^2 - (a^5*b^2 + a^3*b^4)*d + 2*((a^6*b + a^4*b^3)*d*cos(d*x + c)^3 - (a^6*b + a^4*b^3)*d*cos(d*x + c))*sin(d*x + c) - ((a^10 - 3*a^8*b^2 - a^6*b^4 + 3*a^4*b^6)*d^3*cos(d*x + c)^4 - (a^10 - 4*a^8*b^2 + a^6*b^4 + 6*a^4*b^6)*d^3*cos(d*x + c)^2 - (a^8*b^2 - 2*a^6*b^4 - 3*a^4*b^6)*d^3 + 2*((a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c)^3 - (a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^7 - a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - a^5*b^2 - 2*a^3*b^4)*d*cos(d*x + c)^2 - (a^5*b^2 + a^3*b^4)*d + 2*((a^6*b + a^4*b^3)*d*cos(d*x + c)^3 - (a^6*b + a^4*b^3)*d*cos(d*x + c))*sin(d*x + c) - ((a^10 - 3*a^8*b^2 - a^6*b^4 + 3*a^4*b^6)*d^3*cos(d*x + c)^4 - (a^10 - 4*a^8*b^2 + a^6*b^4 + 6*a^4*b^6)*d^3*cos(d*x + c)^2 - (a^8*b^2 - 2*a^6*b^4 - 3*a^4*b^6)*d^3 + 2*((a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c)^3 - (a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) + 3*(a^2*b^3 + b^5 - (a^4*b - b^5)*cos(d*x + c)^4 + (a^4*b - a^2*b^3 - 2*b^5)*cos(d*x + c)^2 - 2*((a^3*b^2 + a*b^4)*cos(d*x + c)^3 - (a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 + 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) + 4*(2*(a^4*b + 2*a^2*b^3)*cos(d*x + c)^4 - 2*(a^4*b + 2*a^2*b^3)*cos(d*x + c)^2 - ((a^5 - 3*a*b^4)*cos(d*x + c)^3 + (a^3*b^2 + 3*a*b^4)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^7 - a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - a^5*b^2 - 2*a^3*b^4)*d*cos(d*x + c)^2 - (a^5*b^2 + a^3*b^4)*d + 2*((a^6*b + a^4*b^3)*d*cos(d*x + c)^3 - (a^6*b + a^4*b^3)*d*cos(d*x + c))*sin(d*x + c)), -1/4*(4*sqrt(2)*((a^13 + 3*a^11*b^2 + 2*a^9*b^4 - 2*a^7*b^6 - 3*a^5*b^8 - a^3*b^10)*d^5*cos(d*x + c)^4 - (a^13 + 2*a^11*b^2 - 2*a^9*b^4 - 8*a^7*b^6 - 7*a^5*b^8 - 2*a^3*b^10)*d^5*cos(d*x + c)^2 - (a^11*b^2 + 4*a^9*b^4 + 6*a^7*b^6 + 4*a^5*b^8 + a^3*b^10)*d^5 + 2*((a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c)^3 - (a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^13 + 3*a^11*b^2 + 2*a^9*b^4 - 2*a^7*b^6 - 3*a^5*b^8 - a^3*b^10)*d^5*cos(d*x + c)^4 - (a^13 + 2*a^11*b^2 - 2*a^9*b^4 - 8*a^7*b^6 - 7*a^5*b^8 - 2*a^3*b^10)*d^5*cos(d*x + c)^2 - (a^11*b^2 + 4*a^9*b^4 + 6*a^7*b^6 + 4*a^5*b^8 + a^3*b^10)*d^5 + 2*((a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c)^3 - (a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*(2*(a^13 + 6*a^11*b^2 + 15*a^9*b^4 + 20*a^7*b^6 + 15*a^5*b^8 + 6*a^3*b^10 + a*b^12)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*(2*(3*a^15*b + 17*a^13*b^3 + 39*a^11*b^5 + 45*a^9*b^7 + 25*a^7*b^9 + 3*a^5*b^11 - 3*a^3*b^13 - a*b^15)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^12*b + 14*a^10*b^3 + 25*a^8*b^5 + 20*a^6*b^7 + 5*a^4*b^9 - 2*a^2*b^11 - b^13)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^7 - a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - a^5*b^2 - 2*a^3*b^4)*d*cos(d*x + c)^2 - (a^5*b^2 + a^3*b^4)*d + 2*((a^6*b + a^4*b^3)*d*cos(d*x + c)^3 - (a^6*b + a^4*b^3)*d*cos(d*x + c))*sin(d*x + c) - ((a^10 - 3*a^8*b^2 - a^6*b^4 + 3*a^4*b^6)*d^3*cos(d*x + c)^4 - (a^10 - 4*a^8*b^2 + a^6*b^4 + 6*a^4*b^6)*d^3*cos(d*x + c)^2 - (a^8*b^2 - 2*a^6*b^4 - 3*a^4*b^6)*d^3 + 2*((a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c)^3 - (a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^7 - a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - a^5*b^2 - 2*a^3*b^4)*d*cos(d*x + c)^2 - (a^5*b^2 + a^3*b^4)*d + 2*((a^6*b + a^4*b^3)*d*cos(d*x + c)^3 - (a^6*b + a^4*b^3)*d*cos(d*x + c))*sin(d*x + c) - ((a^10 - 3*a^8*b^2 - a^6*b^4 + 3*a^4*b^6)*d^3*cos(d*x + c)^4 - (a^10 - 4*a^8*b^2 + a^6*b^4 + 6*a^4*b^6)*d^3*cos(d*x + c)^2 - (a^8*b^2 - 2*a^6*b^4 - 3*a^4*b^6)*d^3 + 2*((a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c)^3 - (a^9*b - 2*a^7*b^3 - 3*a^5*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8*b^2 + 12*a^6*b^4 - 2*a^4*b^6 - 4*a^2*b^8 + b^10)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^8*b^3 + 12*a^6*b^5 - 2*a^4*b^7 - 4*a^2*b^9 + b^11)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + 2*(9*a^5*b^3 - 6*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5*b^2 - 6*a^3*b^4 + a*b^6)*cos(d*x + c) + (9*a^4*b^3 - 6*a^2*b^5 + b^7)*sin(d*x + c))/cos(d*x + c)) - 12*(a^2*b^3 + b^5 - (a^4*b - b^5)*cos(d*x + c)^4 + (a^4*b - a^2*b^3 - 2*b^5)*cos(d*x + c)^2 - 2*((a^3*b^2 + a*b^4)*cos(d*x + c)^3 - (a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) + 4*(2*(a^4*b + 2*a^2*b^3)*cos(d*x + c)^4 - 2*(a^4*b + 2*a^2*b^3)*cos(d*x + c)^2 - ((a^5 - 3*a*b^4)*cos(d*x + c)^3 + (a^3*b^2 + 3*a*b^4)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^7 - a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - a^5*b^2 - 2*a^3*b^4)*d*cos(d*x + c)^2 - (a^5*b^2 + a^3*b^4)*d + 2*((a^6*b + a^4*b^3)*d*cos(d*x + c)^3 - (a^6*b + a^4*b^3)*d*cos(d*x + c))*sin(d*x + c))]","B",0
545,1,13156,0,6.087174," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{16 \, \sqrt{2} {\left({\left(a^{14} + 3 \, a^{12} b^{2} + 2 \, a^{10} b^{4} - 2 \, a^{8} b^{6} - 3 \, a^{6} b^{8} - a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{14} + 2 \, a^{12} b^{2} - 2 \, a^{10} b^{4} - 8 \, a^{8} b^{6} - 7 \, a^{6} b^{8} - 2 \, a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{12} b^{2} + 4 \, a^{10} b^{4} + 6 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + a^{4} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 16 \, \sqrt{2} {\left({\left(a^{14} + 3 \, a^{12} b^{2} + 2 \, a^{10} b^{4} - 2 \, a^{8} b^{6} - 3 \, a^{6} b^{8} - a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{14} + 2 \, a^{12} b^{2} - 2 \, a^{10} b^{4} - 8 \, a^{8} b^{6} - 7 \, a^{6} b^{8} - 2 \, a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{12} b^{2} + 4 \, a^{10} b^{4} + 6 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + a^{4} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{8} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{8} - a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left({\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{11} - 3 \, a^{9} b^{2} - a^{7} b^{4} + 3 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{11} - 4 \, a^{9} b^{2} + a^{7} b^{4} + 6 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, \sqrt{2} {\left({\left(a^{8} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{8} - a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left({\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{11} - 3 \, a^{9} b^{2} - a^{7} b^{4} + 3 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{11} - 4 \, a^{9} b^{2} + a^{7} b^{4} + 6 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - {\left(8 \, a^{4} b^{2} - 7 \, a^{2} b^{4} - 15 \, b^{6} - {\left(8 \, a^{6} - 15 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 15 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, a^{6} - 23 \, a^{4} b^{2} - a^{2} b^{4} + 30 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(8 \, a^{5} b - 7 \, a^{3} b^{3} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(8 \, a^{5} b - 7 \, a^{3} b^{3} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2} - 4 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{\cos\left(d x + c\right)^{2} - 1}\right) - 4 \, {\left(2 \, {\left(a^{6} + 7 \, a^{4} b^{2} + 10 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{4} b^{2} + 5 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(3 \, a^{5} b - 4 \, a^{3} b^{3} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, a^{3} b^{3} + 15 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{16 \, {\left({\left(a^{8} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{8} - a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left({\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}, -\frac{4 \, \sqrt{2} {\left({\left(a^{14} + 3 \, a^{12} b^{2} + 2 \, a^{10} b^{4} - 2 \, a^{8} b^{6} - 3 \, a^{6} b^{8} - a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{14} + 2 \, a^{12} b^{2} - 2 \, a^{10} b^{4} - 8 \, a^{8} b^{6} - 7 \, a^{6} b^{8} - 2 \, a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{12} b^{2} + 4 \, a^{10} b^{4} + 6 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + a^{4} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} + 3 \, a^{12} b^{2} + 2 \, a^{10} b^{4} - 2 \, a^{8} b^{6} - 3 \, a^{6} b^{8} - a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{4} - {\left(a^{14} + 2 \, a^{12} b^{2} - 2 \, a^{10} b^{4} - 8 \, a^{8} b^{6} - 7 \, a^{6} b^{8} - 2 \, a^{4} b^{10}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{12} b^{2} + 4 \, a^{10} b^{4} + 6 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + a^{4} b^{10}\right)} d^{5} + 2 \, {\left({\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)^{3} - {\left(a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(3 \, a^{12} + 14 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 2 \, a^{2} b^{10} - b^{12}\right)} d^{4} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{9} + 8 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - a b^{8}\right)} d^{2} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(a^{11} + 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} + a b^{10}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{16} + 14 \, a^{14} b^{2} + 22 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 20 \, a^{8} b^{8} - 22 \, a^{6} b^{10} - 6 \, a^{4} b^{12} + 2 \, a^{2} b^{14} + b^{16}\right)} d^{7} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} + {\left(3 \, a^{13} + 14 \, a^{11} b^{2} + 25 \, a^{9} b^{4} + 20 \, a^{7} b^{6} + 5 \, a^{5} b^{8} - 2 \, a^{3} b^{10} - a b^{12}\right)} d^{5} \sqrt{\frac{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}{{\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{3}{4}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}\right) + \sqrt{2} {\left({\left(a^{8} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{8} - a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left({\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{11} - 3 \, a^{9} b^{2} - a^{7} b^{4} + 3 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{11} - 4 \, a^{9} b^{2} + a^{7} b^{4} + 6 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{8} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{8} - a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left({\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{11} - 3 \, a^{9} b^{2} - a^{7} b^{4} + 3 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{4} - {\left(a^{11} - 4 \, a^{9} b^{2} + a^{7} b^{4} + 6 \, a^{5} b^{6}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{9} b^{2} - 2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} d^{3} + 2 \, {\left({\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 2 \, a^{8} b^{3} - 3 \, a^{6} b^{5}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(9 \, a^{8} + 12 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(9 \, a^{9} + 12 \, a^{7} b^{2} - 2 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(9 \, a^{6} - 15 \, a^{4} b^{2} + 7 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} - {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}}}{9 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(9 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - {\left(8 \, a^{4} b^{2} - 7 \, a^{2} b^{4} - 15 \, b^{6} - {\left(8 \, a^{6} - 15 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 15 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(8 \, a^{6} - 23 \, a^{4} b^{2} - a^{2} b^{4} + 30 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(8 \, a^{5} b - 7 \, a^{3} b^{3} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(8 \, a^{5} b - 7 \, a^{3} b^{3} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - {\left(2 \, {\left(a^{6} + 7 \, a^{4} b^{2} + 10 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{4} b^{2} + 5 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(3 \, a^{5} b - 4 \, a^{3} b^{3} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(7 \, a^{3} b^{3} + 15 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{8} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{8} - a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left({\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} b + a^{5} b^{3}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(16*sqrt(2)*((a^14 + 3*a^12*b^2 + 2*a^10*b^4 - 2*a^8*b^6 - 3*a^6*b^8 - a^4*b^10)*d^5*cos(d*x + c)^4 - (a^14 + 2*a^12*b^2 - 2*a^10*b^4 - 8*a^8*b^6 - 7*a^6*b^8 - 2*a^4*b^10)*d^5*cos(d*x + c)^2 - (a^12*b^2 + 4*a^10*b^4 + 6*a^8*b^6 + 4*a^6*b^8 + a^4*b^10)*d^5 + 2*((a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c)^3 - (a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 16*sqrt(2)*((a^14 + 3*a^12*b^2 + 2*a^10*b^4 - 2*a^8*b^6 - 3*a^6*b^8 - a^4*b^10)*d^5*cos(d*x + c)^4 - (a^14 + 2*a^12*b^2 - 2*a^10*b^4 - 8*a^8*b^6 - 7*a^6*b^8 - 2*a^4*b^10)*d^5*cos(d*x + c)^2 - (a^12*b^2 + 4*a^10*b^4 + 6*a^8*b^6 + 4*a^6*b^8 + a^4*b^10)*d^5 + 2*((a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c)^3 - (a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^8 - a^4*b^4)*d*cos(d*x + c)^4 - (a^8 - a^6*b^2 - 2*a^4*b^4)*d*cos(d*x + c)^2 - (a^6*b^2 + a^4*b^4)*d + 2*((a^7*b + a^5*b^3)*d*cos(d*x + c)^3 - (a^7*b + a^5*b^3)*d*cos(d*x + c))*sin(d*x + c) + ((a^11 - 3*a^9*b^2 - a^7*b^4 + 3*a^5*b^6)*d^3*cos(d*x + c)^4 - (a^11 - 4*a^9*b^2 + a^7*b^4 + 6*a^5*b^6)*d^3*cos(d*x + c)^2 - (a^9*b^2 - 2*a^7*b^4 - 3*a^5*b^6)*d^3 + 2*((a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c)^3 - (a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - 4*sqrt(2)*((a^8 - a^4*b^4)*d*cos(d*x + c)^4 - (a^8 - a^6*b^2 - 2*a^4*b^4)*d*cos(d*x + c)^2 - (a^6*b^2 + a^4*b^4)*d + 2*((a^7*b + a^5*b^3)*d*cos(d*x + c)^3 - (a^7*b + a^5*b^3)*d*cos(d*x + c))*sin(d*x + c) + ((a^11 - 3*a^9*b^2 - a^7*b^4 + 3*a^5*b^6)*d^3*cos(d*x + c)^4 - (a^11 - 4*a^9*b^2 + a^7*b^4 + 6*a^5*b^6)*d^3*cos(d*x + c)^2 - (a^9*b^2 - 2*a^7*b^4 - 3*a^5*b^6)*d^3 + 2*((a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c)^3 - (a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - (8*a^4*b^2 - 7*a^2*b^4 - 15*b^6 - (8*a^6 - 15*a^4*b^2 - 8*a^2*b^4 + 15*b^6)*cos(d*x + c)^4 + (8*a^6 - 23*a^4*b^2 - a^2*b^4 + 30*b^6)*cos(d*x + c)^2 - 2*((8*a^5*b - 7*a^3*b^3 - 15*a*b^5)*cos(d*x + c)^3 - (8*a^5*b - 7*a^3*b^3 - 15*a*b^5)*cos(d*x + c))*sin(d*x + c))*sqrt(a)*log(-(8*a*b*cos(d*x + c)*sin(d*x + c) + (8*a^2 - b^2)*cos(d*x + c)^2 + b^2 - 4*(2*a*cos(d*x + c)^2 + b*cos(d*x + c)*sin(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(cos(d*x + c)^2 - 1)) - 4*(2*(a^6 + 7*a^4*b^2 + 10*a^2*b^4)*cos(d*x + c)^4 - 4*(3*a^4*b^2 + 5*a^2*b^4)*cos(d*x + c)^2 - ((3*a^5*b - 4*a^3*b^3 - 15*a*b^5)*cos(d*x + c)^3 + (7*a^3*b^3 + 15*a*b^5)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8 - a^4*b^4)*d*cos(d*x + c)^4 - (a^8 - a^6*b^2 - 2*a^4*b^4)*d*cos(d*x + c)^2 - (a^6*b^2 + a^4*b^4)*d + 2*((a^7*b + a^5*b^3)*d*cos(d*x + c)^3 - (a^7*b + a^5*b^3)*d*cos(d*x + c))*sin(d*x + c)), -1/4*(4*sqrt(2)*((a^14 + 3*a^12*b^2 + 2*a^10*b^4 - 2*a^8*b^6 - 3*a^6*b^8 - a^4*b^10)*d^5*cos(d*x + c)^4 - (a^14 + 2*a^12*b^2 - 2*a^10*b^4 - 8*a^8*b^6 - 7*a^6*b^8 - 2*a^4*b^10)*d^5*cos(d*x + c)^2 - (a^12*b^2 + 4*a^10*b^4 + 6*a^8*b^6 + 4*a^6*b^8 + a^4*b^10)*d^5 + 2*((a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c)^3 - (a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(-((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) + sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) + sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + 4*sqrt(2)*((a^14 + 3*a^12*b^2 + 2*a^10*b^4 - 2*a^8*b^6 - 3*a^6*b^8 - a^4*b^10)*d^5*cos(d*x + c)^4 - (a^14 + 2*a^12*b^2 - 2*a^10*b^4 - 8*a^8*b^6 - 7*a^6*b^8 - 2*a^4*b^10)*d^5*cos(d*x + c)^2 - (a^12*b^2 + 4*a^10*b^4 + 6*a^8*b^6 + 4*a^6*b^8 + a^4*b^10)*d^5 + 2*((a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c)^3 - (a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4)*arctan(((3*a^12 + 14*a^10*b^2 + 25*a^8*b^4 + 20*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12)*d^4*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^9 + 8*a^7*b^2 + 6*a^5*b^4 - a*b^8)*d^2*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)) - sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (a^11 + 5*a^9*b^2 + 10*a^7*b^4 + 10*a^5*b^6 + 5*a^3*b^8 + a*b^10)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4) - sqrt(2)*((3*a^16 + 14*a^14*b^2 + 22*a^12*b^4 + 6*a^10*b^6 - 20*a^8*b^8 - 22*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 + b^16)*d^7*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)) + (3*a^13 + 14*a^11*b^2 + 25*a^9*b^4 + 20*a^7*b^6 + 5*a^5*b^8 - 2*a^3*b^10 - a*b^12)*d^5*sqrt((9*a^4*b^2 - 6*a^2*b^4 + b^6)/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(3/4))/(9*a^4*b^2 - 6*a^2*b^4 + b^6)) + sqrt(2)*((a^8 - a^4*b^4)*d*cos(d*x + c)^4 - (a^8 - a^6*b^2 - 2*a^4*b^4)*d*cos(d*x + c)^2 - (a^6*b^2 + a^4*b^4)*d + 2*((a^7*b + a^5*b^3)*d*cos(d*x + c)^3 - (a^7*b + a^5*b^3)*d*cos(d*x + c))*sin(d*x + c) + ((a^11 - 3*a^9*b^2 - a^7*b^4 + 3*a^5*b^6)*d^3*cos(d*x + c)^4 - (a^11 - 4*a^9*b^2 + a^7*b^4 + 6*a^5*b^6)*d^3*cos(d*x + c)^2 - (a^9*b^2 - 2*a^7*b^4 - 3*a^5*b^6)*d^3 + 2*((a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c)^3 - (a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^8 - a^4*b^4)*d*cos(d*x + c)^4 - (a^8 - a^6*b^2 - 2*a^4*b^4)*d*cos(d*x + c)^2 - (a^6*b^2 + a^4*b^4)*d + 2*((a^7*b + a^5*b^3)*d*cos(d*x + c)^3 - (a^7*b + a^5*b^3)*d*cos(d*x + c))*sin(d*x + c) + ((a^11 - 3*a^9*b^2 - a^7*b^4 + 3*a^5*b^6)*d^3*cos(d*x + c)^4 - (a^11 - 4*a^9*b^2 + a^7*b^4 + 6*a^5*b^6)*d^3*cos(d*x + c)^2 - (a^9*b^2 - 2*a^7*b^4 - 3*a^5*b^6)*d^3 + 2*((a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c)^3 - (a^10*b - 2*a^8*b^3 - 3*a^6*b^5)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4)*log(((9*a^8 + 12*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) - sqrt(2)*((9*a^9 + 12*a^7*b^2 - 2*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d^3*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))*cos(d*x + c) + (9*a^6 - 15*a^4*b^2 + 7*a^2*b^4 - b^6)*d*cos(d*x + c))*sqrt((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 - (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^2*sqrt(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4)))/(9*a^4*b^2 - 6*a^2*b^4 + b^6))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4))^(1/4) + (9*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c) + (9*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))/cos(d*x + c)) - (8*a^4*b^2 - 7*a^2*b^4 - 15*b^6 - (8*a^6 - 15*a^4*b^2 - 8*a^2*b^4 + 15*b^6)*cos(d*x + c)^4 + (8*a^6 - 23*a^4*b^2 - a^2*b^4 + 30*b^6)*cos(d*x + c)^2 - 2*((8*a^5*b - 7*a^3*b^3 - 15*a*b^5)*cos(d*x + c)^3 - (8*a^5*b - 7*a^3*b^3 - 15*a*b^5)*cos(d*x + c))*sin(d*x + c))*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))/a) - (2*(a^6 + 7*a^4*b^2 + 10*a^2*b^4)*cos(d*x + c)^4 - 4*(3*a^4*b^2 + 5*a^2*b^4)*cos(d*x + c)^2 - ((3*a^5*b - 4*a^3*b^3 - 15*a*b^5)*cos(d*x + c)^3 + (7*a^3*b^3 + 15*a*b^5)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8 - a^4*b^4)*d*cos(d*x + c)^4 - (a^8 - a^6*b^2 - 2*a^4*b^4)*d*cos(d*x + c)^2 - (a^6*b^2 + a^4*b^4)*d + 2*((a^7*b + a^5*b^3)*d*cos(d*x + c)^3 - (a^7*b + a^5*b^3)*d*cos(d*x + c))*sin(d*x + c))]","B",0
546,1,10005,0,2.981197," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(a^{18} b^{4} + a^{16} b^{6} - 20 \, a^{14} b^{8} - 84 \, a^{12} b^{10} - 154 \, a^{10} b^{12} - 154 \, a^{8} b^{14} - 84 \, a^{6} b^{16} - 20 \, a^{4} b^{18} + a^{2} b^{20} + b^{22}\right)} d^{5} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{16} b^{6} + 20 \, a^{14} b^{8} + 56 \, a^{12} b^{10} + 84 \, a^{10} b^{12} + 70 \, a^{8} b^{14} + 28 \, a^{6} b^{16} - 4 \, a^{2} b^{20} - b^{22}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{14} b^{8} + 7 \, a^{12} b^{10} + 21 \, a^{10} b^{12} + 35 \, a^{8} b^{14} + 35 \, a^{6} b^{16} + 21 \, a^{4} b^{18} + 7 \, a^{2} b^{20} + b^{22}\right)} d^{5} \cos\left(d x + c\right) + 4 \, {\left({\left(a^{17} b^{5} + 6 \, a^{15} b^{7} + 14 \, a^{13} b^{9} + 14 \, a^{11} b^{11} - 14 \, a^{7} b^{15} - 14 \, a^{5} b^{17} - 6 \, a^{3} b^{19} - a b^{21}\right)} d^{5} \cos\left(d x + c\right)^{4} + {\left(a^{15} b^{7} + 7 \, a^{13} b^{9} + 21 \, a^{11} b^{11} + 35 \, a^{9} b^{13} + 35 \, a^{7} b^{15} + 21 \, a^{5} b^{17} + 7 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{23} + 7 \, a^{21} b^{2} + 15 \, a^{19} b^{4} - 15 \, a^{17} b^{6} - 150 \, a^{15} b^{8} - 378 \, a^{13} b^{10} - 546 \, a^{11} b^{12} - 510 \, a^{9} b^{14} - 315 \, a^{7} b^{16} - 125 \, a^{5} b^{18} - 29 \, a^{3} b^{20} - 3 \, a b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(5 \, a^{27} + 25 \, a^{25} b^{2} + 6 \, a^{23} b^{4} - 218 \, a^{21} b^{6} - 585 \, a^{19} b^{8} - 405 \, a^{17} b^{10} + 900 \, a^{15} b^{12} + 2532 \, a^{13} b^{14} + 2979 \, a^{11} b^{16} + 2015 \, a^{9} b^{18} + 790 \, a^{7} b^{20} + 150 \, a^{5} b^{22} + a^{3} b^{24} - 3 \, a b^{26}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{22} + 25 \, a^{20} b^{2} + 31 \, a^{18} b^{4} - 53 \, a^{16} b^{6} - 190 \, a^{14} b^{8} - 182 \, a^{12} b^{10} + 14 \, a^{10} b^{12} + 166 \, a^{8} b^{14} + 137 \, a^{6} b^{16} + 45 \, a^{4} b^{18} + 3 \, a^{2} b^{20} - b^{22}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 12 \, \sqrt{2} {\left({\left(a^{18} b^{4} + a^{16} b^{6} - 20 \, a^{14} b^{8} - 84 \, a^{12} b^{10} - 154 \, a^{10} b^{12} - 154 \, a^{8} b^{14} - 84 \, a^{6} b^{16} - 20 \, a^{4} b^{18} + a^{2} b^{20} + b^{22}\right)} d^{5} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{16} b^{6} + 20 \, a^{14} b^{8} + 56 \, a^{12} b^{10} + 84 \, a^{10} b^{12} + 70 \, a^{8} b^{14} + 28 \, a^{6} b^{16} - 4 \, a^{2} b^{20} - b^{22}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{14} b^{8} + 7 \, a^{12} b^{10} + 21 \, a^{10} b^{12} + 35 \, a^{8} b^{14} + 35 \, a^{6} b^{16} + 21 \, a^{4} b^{18} + 7 \, a^{2} b^{20} + b^{22}\right)} d^{5} \cos\left(d x + c\right) + 4 \, {\left({\left(a^{17} b^{5} + 6 \, a^{15} b^{7} + 14 \, a^{13} b^{9} + 14 \, a^{11} b^{11} - 14 \, a^{7} b^{15} - 14 \, a^{5} b^{17} - 6 \, a^{3} b^{19} - a b^{21}\right)} d^{5} \cos\left(d x + c\right)^{4} + {\left(a^{15} b^{7} + 7 \, a^{13} b^{9} + 21 \, a^{11} b^{11} + 35 \, a^{9} b^{13} + 35 \, a^{7} b^{15} + 21 \, a^{5} b^{17} + 7 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{23} + 7 \, a^{21} b^{2} + 15 \, a^{19} b^{4} - 15 \, a^{17} b^{6} - 150 \, a^{15} b^{8} - 378 \, a^{13} b^{10} - 546 \, a^{11} b^{12} - 510 \, a^{9} b^{14} - 315 \, a^{7} b^{16} - 125 \, a^{5} b^{18} - 29 \, a^{3} b^{20} - 3 \, a b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(5 \, a^{27} + 25 \, a^{25} b^{2} + 6 \, a^{23} b^{4} - 218 \, a^{21} b^{6} - 585 \, a^{19} b^{8} - 405 \, a^{17} b^{10} + 900 \, a^{15} b^{12} + 2532 \, a^{13} b^{14} + 2979 \, a^{11} b^{16} + 2015 \, a^{9} b^{18} + 790 \, a^{7} b^{20} + 150 \, a^{5} b^{22} + a^{3} b^{24} - 3 \, a b^{26}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{22} + 25 \, a^{20} b^{2} + 31 \, a^{18} b^{4} - 53 \, a^{16} b^{6} - 190 \, a^{14} b^{8} - 182 \, a^{12} b^{10} + 14 \, a^{10} b^{12} + 166 \, a^{8} b^{14} + 137 \, a^{6} b^{16} + 45 \, a^{4} b^{18} + 3 \, a^{2} b^{20} - b^{22}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} - 10 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right) + 4 \, {\left({\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{5} b^{7} + 2 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right) + {\left({\left(a^{13} b^{4} - 14 \, a^{11} b^{6} + 35 \, a^{9} b^{8} + 76 \, a^{7} b^{10} - 9 \, a^{5} b^{12} - 30 \, a^{3} b^{14} + 5 \, a b^{16}\right)} d^{3} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{11} b^{6} - 25 \, a^{9} b^{8} - 34 \, a^{7} b^{10} + 14 \, a^{5} b^{12} + 15 \, a^{3} b^{14} - 5 \, a b^{16}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{9} b^{8} - 8 \, a^{7} b^{10} - 14 \, a^{5} b^{12} + 5 \, a b^{16}\right)} d^{3} \cos\left(d x + c\right) + 4 \, {\left({\left(a^{12} b^{5} - 9 \, a^{10} b^{7} - 6 \, a^{8} b^{9} + 14 \, a^{6} b^{11} + 5 \, a^{4} b^{13} - 5 \, a^{2} b^{15}\right)} d^{3} \cos\left(d x + c\right)^{4} + {\left(a^{10} b^{7} - 8 \, a^{8} b^{9} - 14 \, a^{6} b^{11} + 5 \, a^{2} b^{15}\right)} d^{3} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} - 10 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right) + 4 \, {\left({\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{5} b^{7} + 2 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right) + {\left({\left(a^{13} b^{4} - 14 \, a^{11} b^{6} + 35 \, a^{9} b^{8} + 76 \, a^{7} b^{10} - 9 \, a^{5} b^{12} - 30 \, a^{3} b^{14} + 5 \, a b^{16}\right)} d^{3} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{11} b^{6} - 25 \, a^{9} b^{8} - 34 \, a^{7} b^{10} + 14 \, a^{5} b^{12} + 15 \, a^{3} b^{14} - 5 \, a b^{16}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{9} b^{8} - 8 \, a^{7} b^{10} - 14 \, a^{5} b^{12} + 5 \, a b^{16}\right)} d^{3} \cos\left(d x + c\right) + 4 \, {\left({\left(a^{12} b^{5} - 9 \, a^{10} b^{7} - 6 \, a^{8} b^{9} + 14 \, a^{6} b^{11} + 5 \, a^{4} b^{13} - 5 \, a^{2} b^{15}\right)} d^{3} \cos\left(d x + c\right)^{4} + {\left(a^{10} b^{7} - 8 \, a^{8} b^{9} - 14 \, a^{6} b^{11} + 5 \, a^{2} b^{15}\right)} d^{3} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(4 \, {\left(4 \, a^{9} - 10 \, a^{7} b^{2} - 30 \, a^{5} b^{4} - 9 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{7} b^{2} + 62 \, a^{5} b^{4} + 14 \, a^{3} b^{6} - 4 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) - {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9} - {\left(56 \, a^{8} b + 70 \, a^{6} b^{3} - 37 \, a^{4} b^{5} - 28 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(35 \, a^{6} b^{3} + 69 \, a^{4} b^{5} + 30 \, a^{2} b^{7} + 2 \, b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} - 10 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right) + 4 \, {\left({\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{5} b^{7} + 2 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(12*sqrt(2)*((a^18*b^4 + a^16*b^6 - 20*a^14*b^8 - 84*a^12*b^10 - 154*a^10*b^12 - 154*a^8*b^14 - 84*a^6*b^16 - 20*a^4*b^18 + a^2*b^20 + b^22)*d^5*cos(d*x + c)^5 + 2*(3*a^16*b^6 + 20*a^14*b^8 + 56*a^12*b^10 + 84*a^10*b^12 + 70*a^8*b^14 + 28*a^6*b^16 - 4*a^2*b^20 - b^22)*d^5*cos(d*x + c)^3 + (a^14*b^8 + 7*a^12*b^10 + 21*a^10*b^12 + 35*a^8*b^14 + 35*a^6*b^16 + 21*a^4*b^18 + 7*a^2*b^20 + b^22)*d^5*cos(d*x + c) + 4*((a^17*b^5 + 6*a^15*b^7 + 14*a^13*b^9 + 14*a^11*b^11 - 14*a^7*b^15 - 14*a^5*b^17 - 6*a^3*b^19 - a*b^21)*d^5*cos(d*x + c)^4 + (a^15*b^7 + 7*a^13*b^9 + 21*a^11*b^11 + 35*a^9*b^13 + 35*a^7*b^15 + 21*a^5*b^17 + 7*a^3*b^19 + a*b^21)*d^5*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) - sqrt(2)*((a^23 + 7*a^21*b^2 + 15*a^19*b^4 - 15*a^17*b^6 - 150*a^15*b^8 - 378*a^13*b^10 - 546*a^11*b^12 - 510*a^9*b^14 - 315*a^7*b^16 - 125*a^5*b^18 - 29*a^3*b^20 - 3*a*b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) + sqrt(2)*((5*a^27 + 25*a^25*b^2 + 6*a^23*b^4 - 218*a^21*b^6 - 585*a^19*b^8 - 405*a^17*b^10 + 900*a^15*b^12 + 2532*a^13*b^14 + 2979*a^11*b^16 + 2015*a^9*b^18 + 790*a^7*b^20 + 150*a^5*b^22 + a^3*b^24 - 3*a*b^26)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^22 + 25*a^20*b^2 + 31*a^18*b^4 - 53*a^16*b^6 - 190*a^14*b^8 - 182*a^12*b^10 + 14*a^10*b^12 + 166*a^8*b^14 + 137*a^6*b^16 + 45*a^4*b^18 + 3*a^2*b^20 - b^22)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 12*sqrt(2)*((a^18*b^4 + a^16*b^6 - 20*a^14*b^8 - 84*a^12*b^10 - 154*a^10*b^12 - 154*a^8*b^14 - 84*a^6*b^16 - 20*a^4*b^18 + a^2*b^20 + b^22)*d^5*cos(d*x + c)^5 + 2*(3*a^16*b^6 + 20*a^14*b^8 + 56*a^12*b^10 + 84*a^10*b^12 + 70*a^8*b^14 + 28*a^6*b^16 - 4*a^2*b^20 - b^22)*d^5*cos(d*x + c)^3 + (a^14*b^8 + 7*a^12*b^10 + 21*a^10*b^12 + 35*a^8*b^14 + 35*a^6*b^16 + 21*a^4*b^18 + 7*a^2*b^20 + b^22)*d^5*cos(d*x + c) + 4*((a^17*b^5 + 6*a^15*b^7 + 14*a^13*b^9 + 14*a^11*b^11 - 14*a^7*b^15 - 14*a^5*b^17 - 6*a^3*b^19 - a*b^21)*d^5*cos(d*x + c)^4 + (a^15*b^7 + 7*a^13*b^9 + 21*a^11*b^11 + 35*a^9*b^13 + 35*a^7*b^15 + 21*a^5*b^17 + 7*a^3*b^19 + a*b^21)*d^5*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(-((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) + sqrt(2)*((a^23 + 7*a^21*b^2 + 15*a^19*b^4 - 15*a^17*b^6 - 150*a^15*b^8 - 378*a^13*b^10 - 546*a^11*b^12 - 510*a^9*b^14 - 315*a^7*b^16 - 125*a^5*b^18 - 29*a^3*b^20 - 3*a*b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) - sqrt(2)*((5*a^27 + 25*a^25*b^2 + 6*a^23*b^4 - 218*a^21*b^6 - 585*a^19*b^8 - 405*a^17*b^10 + 900*a^15*b^12 + 2532*a^13*b^14 + 2979*a^11*b^16 + 2015*a^9*b^18 + 790*a^7*b^20 + 150*a^5*b^22 + a^3*b^24 - 3*a*b^26)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^22 + 25*a^20*b^2 + 31*a^18*b^4 - 53*a^16*b^6 - 190*a^14*b^8 - 182*a^12*b^10 + 14*a^10*b^12 + 166*a^8*b^14 + 137*a^6*b^16 + 45*a^4*b^18 + 3*a^2*b^20 - b^22)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) - 3*sqrt(2)*((a^8*b^4 - 4*a^6*b^6 - 10*a^4*b^8 - 4*a^2*b^10 + b^12)*d*cos(d*x + c)^5 + 2*(3*a^6*b^6 + 5*a^4*b^8 + a^2*b^10 - b^12)*d*cos(d*x + c)^3 + (a^4*b^8 + 2*a^2*b^10 + b^12)*d*cos(d*x + c) + 4*((a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d*cos(d*x + c)^4 + (a^5*b^7 + 2*a^3*b^9 + a*b^11)*d*cos(d*x + c)^2)*sin(d*x + c) + ((a^13*b^4 - 14*a^11*b^6 + 35*a^9*b^8 + 76*a^7*b^10 - 9*a^5*b^12 - 30*a^3*b^14 + 5*a*b^16)*d^3*cos(d*x + c)^5 + 2*(3*a^11*b^6 - 25*a^9*b^8 - 34*a^7*b^10 + 14*a^5*b^12 + 15*a^3*b^14 - 5*a*b^16)*d^3*cos(d*x + c)^3 + (a^9*b^8 - 8*a^7*b^10 - 14*a^5*b^12 + 5*a*b^16)*d^3*cos(d*x + c) + 4*((a^12*b^5 - 9*a^10*b^7 - 6*a^8*b^9 + 14*a^6*b^11 + 5*a^4*b^13 - 5*a^2*b^15)*d^3*cos(d*x + c)^4 + (a^10*b^7 - 8*a^8*b^9 - 14*a^6*b^11 + 5*a^2*b^15)*d^3*cos(d*x + c)^2)*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^8*b^4 - 4*a^6*b^6 - 10*a^4*b^8 - 4*a^2*b^10 + b^12)*d*cos(d*x + c)^5 + 2*(3*a^6*b^6 + 5*a^4*b^8 + a^2*b^10 - b^12)*d*cos(d*x + c)^3 + (a^4*b^8 + 2*a^2*b^10 + b^12)*d*cos(d*x + c) + 4*((a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d*cos(d*x + c)^4 + (a^5*b^7 + 2*a^3*b^9 + a*b^11)*d*cos(d*x + c)^2)*sin(d*x + c) + ((a^13*b^4 - 14*a^11*b^6 + 35*a^9*b^8 + 76*a^7*b^10 - 9*a^5*b^12 - 30*a^3*b^14 + 5*a*b^16)*d^3*cos(d*x + c)^5 + 2*(3*a^11*b^6 - 25*a^9*b^8 - 34*a^7*b^10 + 14*a^5*b^12 + 15*a^3*b^14 - 5*a*b^16)*d^3*cos(d*x + c)^3 + (a^9*b^8 - 8*a^7*b^10 - 14*a^5*b^12 + 5*a*b^16)*d^3*cos(d*x + c) + 4*((a^12*b^5 - 9*a^10*b^7 - 6*a^8*b^9 + 14*a^6*b^11 + 5*a^4*b^13 - 5*a^2*b^15)*d^3*cos(d*x + c)^4 + (a^10*b^7 - 8*a^8*b^9 - 14*a^6*b^11 + 5*a^2*b^15)*d^3*cos(d*x + c)^2)*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c)) - 8*(4*(4*a^9 - 10*a^7*b^2 - 30*a^5*b^4 - 9*a^3*b^6 + a*b^8)*cos(d*x + c)^5 + 2*(35*a^7*b^2 + 62*a^5*b^4 + 14*a^3*b^6 - 4*a*b^8)*cos(d*x + c)^3 + 4*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*cos(d*x + c) - (a^4*b^5 + 2*a^2*b^7 + b^9 - (56*a^8*b + 70*a^6*b^3 - 37*a^4*b^5 - 28*a^2*b^7 - b^9)*cos(d*x + c)^4 - (35*a^6*b^3 + 69*a^4*b^5 + 30*a^2*b^7 + 2*b^9)*cos(d*x + c)^2)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8*b^4 - 4*a^6*b^6 - 10*a^4*b^8 - 4*a^2*b^10 + b^12)*d*cos(d*x + c)^5 + 2*(3*a^6*b^6 + 5*a^4*b^8 + a^2*b^10 - b^12)*d*cos(d*x + c)^3 + (a^4*b^8 + 2*a^2*b^10 + b^12)*d*cos(d*x + c) + 4*((a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d*cos(d*x + c)^4 + (a^5*b^7 + 2*a^3*b^9 + a*b^11)*d*cos(d*x + c)^2)*sin(d*x + c))","B",0
547,1,9896,0,3.625175," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(a^{18} b^{3} + a^{16} b^{5} - 20 \, a^{14} b^{7} - 84 \, a^{12} b^{9} - 154 \, a^{10} b^{11} - 154 \, a^{8} b^{13} - 84 \, a^{6} b^{15} - 20 \, a^{4} b^{17} + a^{2} b^{19} + b^{21}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{5} + 20 \, a^{14} b^{7} + 56 \, a^{12} b^{9} + 84 \, a^{10} b^{11} + 70 \, a^{8} b^{13} + 28 \, a^{6} b^{15} - 4 \, a^{2} b^{19} - b^{21}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{7} + 7 \, a^{12} b^{9} + 21 \, a^{10} b^{11} + 35 \, a^{8} b^{13} + 35 \, a^{6} b^{15} + 21 \, a^{4} b^{17} + 7 \, a^{2} b^{19} + b^{21}\right)} d^{5} + 4 \, {\left({\left(a^{17} b^{4} + 6 \, a^{15} b^{6} + 14 \, a^{13} b^{8} + 14 \, a^{11} b^{10} - 14 \, a^{7} b^{14} - 14 \, a^{5} b^{16} - 6 \, a^{3} b^{18} - a b^{20}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{6} + 7 \, a^{13} b^{8} + 21 \, a^{11} b^{10} + 35 \, a^{9} b^{12} + 35 \, a^{7} b^{14} + 21 \, a^{5} b^{16} + 7 \, a^{3} b^{18} + a b^{20}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{22} + 29 \, a^{20} b^{2} + 125 \, a^{18} b^{4} + 315 \, a^{16} b^{6} + 510 \, a^{14} b^{8} + 546 \, a^{12} b^{10} + 378 \, a^{10} b^{12} + 150 \, a^{8} b^{14} + 15 \, a^{6} b^{16} - 15 \, a^{4} b^{18} - 7 \, a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(a^{17} + 8 \, a^{15} b^{2} + 28 \, a^{13} b^{4} + 56 \, a^{11} b^{6} + 70 \, a^{9} b^{8} + 56 \, a^{7} b^{10} + 28 \, a^{5} b^{12} + 8 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(15 \, a^{26} b + 115 \, a^{24} b^{3} + 338 \, a^{22} b^{5} + 354 \, a^{20} b^{7} - 475 \, a^{18} b^{9} - 2055 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} - 2484 \, a^{12} b^{15} - 1047 \, a^{10} b^{17} - 75 \, a^{8} b^{19} + 130 \, a^{6} b^{21} + 50 \, a^{4} b^{23} + 3 \, a^{2} b^{25} - b^{27}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(5 \, a^{21} b + 30 \, a^{19} b^{3} + 61 \, a^{17} b^{5} + 8 \, a^{15} b^{7} - 182 \, a^{13} b^{9} - 364 \, a^{11} b^{11} - 350 \, a^{9} b^{13} - 184 \, a^{7} b^{15} - 47 \, a^{5} b^{17} - 2 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 12 \, \sqrt{2} {\left({\left(a^{18} b^{3} + a^{16} b^{5} - 20 \, a^{14} b^{7} - 84 \, a^{12} b^{9} - 154 \, a^{10} b^{11} - 154 \, a^{8} b^{13} - 84 \, a^{6} b^{15} - 20 \, a^{4} b^{17} + a^{2} b^{19} + b^{21}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{5} + 20 \, a^{14} b^{7} + 56 \, a^{12} b^{9} + 84 \, a^{10} b^{11} + 70 \, a^{8} b^{13} + 28 \, a^{6} b^{15} - 4 \, a^{2} b^{19} - b^{21}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{7} + 7 \, a^{12} b^{9} + 21 \, a^{10} b^{11} + 35 \, a^{8} b^{13} + 35 \, a^{6} b^{15} + 21 \, a^{4} b^{17} + 7 \, a^{2} b^{19} + b^{21}\right)} d^{5} + 4 \, {\left({\left(a^{17} b^{4} + 6 \, a^{15} b^{6} + 14 \, a^{13} b^{8} + 14 \, a^{11} b^{10} - 14 \, a^{7} b^{14} - 14 \, a^{5} b^{16} - 6 \, a^{3} b^{18} - a b^{20}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{6} + 7 \, a^{13} b^{8} + 21 \, a^{11} b^{10} + 35 \, a^{9} b^{12} + 35 \, a^{7} b^{14} + 21 \, a^{5} b^{16} + 7 \, a^{3} b^{18} + a b^{20}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{22} + 29 \, a^{20} b^{2} + 125 \, a^{18} b^{4} + 315 \, a^{16} b^{6} + 510 \, a^{14} b^{8} + 546 \, a^{12} b^{10} + 378 \, a^{10} b^{12} + 150 \, a^{8} b^{14} + 15 \, a^{6} b^{16} - 15 \, a^{4} b^{18} - 7 \, a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(a^{17} + 8 \, a^{15} b^{2} + 28 \, a^{13} b^{4} + 56 \, a^{11} b^{6} + 70 \, a^{9} b^{8} + 56 \, a^{7} b^{10} + 28 \, a^{5} b^{12} + 8 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(15 \, a^{26} b + 115 \, a^{24} b^{3} + 338 \, a^{22} b^{5} + 354 \, a^{20} b^{7} - 475 \, a^{18} b^{9} - 2055 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} - 2484 \, a^{12} b^{15} - 1047 \, a^{10} b^{17} - 75 \, a^{8} b^{19} + 130 \, a^{6} b^{21} + 50 \, a^{4} b^{23} + 3 \, a^{2} b^{25} - b^{27}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(5 \, a^{21} b + 30 \, a^{19} b^{3} + 61 \, a^{17} b^{5} + 8 \, a^{15} b^{7} - 182 \, a^{13} b^{9} - 364 \, a^{11} b^{11} - 350 \, a^{9} b^{13} - 184 \, a^{7} b^{15} - 47 \, a^{5} b^{17} - 2 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} - 10 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{5} + 5 \, a^{4} b^{7} + a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{7} + 2 \, a^{2} b^{9} + b^{11}\right)} d + 4 \, {\left({\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{6} + 2 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{13} b^{3} - 14 \, a^{11} b^{5} + 35 \, a^{9} b^{7} + 76 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 30 \, a^{3} b^{13} + 5 \, a b^{15}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{5} - 25 \, a^{9} b^{7} - 34 \, a^{7} b^{9} + 14 \, a^{5} b^{11} + 15 \, a^{3} b^{13} - 5 \, a b^{15}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{7} - 8 \, a^{7} b^{9} - 14 \, a^{5} b^{11} + 5 \, a b^{15}\right)} d^{3} + 4 \, {\left({\left(a^{12} b^{4} - 9 \, a^{10} b^{6} - 6 \, a^{8} b^{8} + 14 \, a^{6} b^{10} + 5 \, a^{4} b^{12} - 5 \, a^{2} b^{14}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{6} - 8 \, a^{8} b^{8} - 14 \, a^{6} b^{10} + 5 \, a^{2} b^{14}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} - 10 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{5} + 5 \, a^{4} b^{7} + a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{7} + 2 \, a^{2} b^{9} + b^{11}\right)} d + 4 \, {\left({\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{6} + 2 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{13} b^{3} - 14 \, a^{11} b^{5} + 35 \, a^{9} b^{7} + 76 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 30 \, a^{3} b^{13} + 5 \, a b^{15}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{5} - 25 \, a^{9} b^{7} - 34 \, a^{7} b^{9} + 14 \, a^{5} b^{11} + 15 \, a^{3} b^{13} - 5 \, a b^{15}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{7} - 8 \, a^{7} b^{9} - 14 \, a^{5} b^{11} + 5 \, a b^{15}\right)} d^{3} + 4 \, {\left({\left(a^{12} b^{4} - 9 \, a^{10} b^{6} - 6 \, a^{8} b^{8} + 14 \, a^{6} b^{10} + 5 \, a^{4} b^{12} - 5 \, a^{2} b^{14}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{6} - 8 \, a^{8} b^{8} - 14 \, a^{6} b^{10} + 5 \, a^{2} b^{14}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(3 \, a^{4} b^{4} + 6 \, a^{2} b^{6} + 3 \, b^{8} + {\left(8 \, a^{8} - 18 \, a^{6} b^{2} - 65 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + 3 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(35 \, a^{6} b^{2} + 65 \, a^{4} b^{4} + 6 \, a^{2} b^{6} - 6 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(7 \, a^{7} b + 10 \, a^{5} b^{3} - 6 \, a^{3} b^{5} - 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{5} b^{3} + 6 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} - 10 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{5} + 5 \, a^{4} b^{7} + a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{7} + 2 \, a^{2} b^{9} + b^{11}\right)} d + 4 \, {\left({\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{6} + 2 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(12*sqrt(2)*((a^18*b^3 + a^16*b^5 - 20*a^14*b^7 - 84*a^12*b^9 - 154*a^10*b^11 - 154*a^8*b^13 - 84*a^6*b^15 - 20*a^4*b^17 + a^2*b^19 + b^21)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^5 + 20*a^14*b^7 + 56*a^12*b^9 + 84*a^10*b^11 + 70*a^8*b^13 + 28*a^6*b^15 - 4*a^2*b^19 - b^21)*d^5*cos(d*x + c)^2 + (a^14*b^7 + 7*a^12*b^9 + 21*a^10*b^11 + 35*a^8*b^13 + 35*a^6*b^15 + 21*a^4*b^17 + 7*a^2*b^19 + b^21)*d^5 + 4*((a^17*b^4 + 6*a^15*b^6 + 14*a^13*b^8 + 14*a^11*b^10 - 14*a^7*b^14 - 14*a^5*b^16 - 6*a^3*b^18 - a*b^20)*d^5*cos(d*x + c)^3 + (a^15*b^6 + 7*a^13*b^8 + 21*a^11*b^10 + 35*a^9*b^12 + 35*a^7*b^14 + 21*a^5*b^16 + 7*a^3*b^18 + a*b^20)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) - sqrt(2)*((3*a^22 + 29*a^20*b^2 + 125*a^18*b^4 + 315*a^16*b^6 + 510*a^14*b^8 + 546*a^12*b^10 + 378*a^10*b^12 + 150*a^8*b^14 + 15*a^6*b^16 - 15*a^4*b^18 - 7*a^2*b^20 - b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(a^17 + 8*a^15*b^2 + 28*a^13*b^4 + 56*a^11*b^6 + 70*a^9*b^8 + 56*a^7*b^10 + 28*a^5*b^12 + 8*a^3*b^14 + a*b^16)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) + sqrt(2)*((15*a^26*b + 115*a^24*b^3 + 338*a^22*b^5 + 354*a^20*b^7 - 475*a^18*b^9 - 2055*a^16*b^11 - 3060*a^14*b^13 - 2484*a^12*b^15 - 1047*a^10*b^17 - 75*a^8*b^19 + 130*a^6*b^21 + 50*a^4*b^23 + 3*a^2*b^25 - b^27)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(5*a^21*b + 30*a^19*b^3 + 61*a^17*b^5 + 8*a^15*b^7 - 182*a^13*b^9 - 364*a^11*b^11 - 350*a^9*b^13 - 184*a^7*b^15 - 47*a^5*b^17 - 2*a^3*b^19 + a*b^21)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 12*sqrt(2)*((a^18*b^3 + a^16*b^5 - 20*a^14*b^7 - 84*a^12*b^9 - 154*a^10*b^11 - 154*a^8*b^13 - 84*a^6*b^15 - 20*a^4*b^17 + a^2*b^19 + b^21)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^5 + 20*a^14*b^7 + 56*a^12*b^9 + 84*a^10*b^11 + 70*a^8*b^13 + 28*a^6*b^15 - 4*a^2*b^19 - b^21)*d^5*cos(d*x + c)^2 + (a^14*b^7 + 7*a^12*b^9 + 21*a^10*b^11 + 35*a^8*b^13 + 35*a^6*b^15 + 21*a^4*b^17 + 7*a^2*b^19 + b^21)*d^5 + 4*((a^17*b^4 + 6*a^15*b^6 + 14*a^13*b^8 + 14*a^11*b^10 - 14*a^7*b^14 - 14*a^5*b^16 - 6*a^3*b^18 - a*b^20)*d^5*cos(d*x + c)^3 + (a^15*b^6 + 7*a^13*b^8 + 21*a^11*b^10 + 35*a^9*b^12 + 35*a^7*b^14 + 21*a^5*b^16 + 7*a^3*b^18 + a*b^20)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(-((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) + sqrt(2)*((3*a^22 + 29*a^20*b^2 + 125*a^18*b^4 + 315*a^16*b^6 + 510*a^14*b^8 + 546*a^12*b^10 + 378*a^10*b^12 + 150*a^8*b^14 + 15*a^6*b^16 - 15*a^4*b^18 - 7*a^2*b^20 - b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(a^17 + 8*a^15*b^2 + 28*a^13*b^4 + 56*a^11*b^6 + 70*a^9*b^8 + 56*a^7*b^10 + 28*a^5*b^12 + 8*a^3*b^14 + a*b^16)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) - sqrt(2)*((15*a^26*b + 115*a^24*b^3 + 338*a^22*b^5 + 354*a^20*b^7 - 475*a^18*b^9 - 2055*a^16*b^11 - 3060*a^14*b^13 - 2484*a^12*b^15 - 1047*a^10*b^17 - 75*a^8*b^19 + 130*a^6*b^21 + 50*a^4*b^23 + 3*a^2*b^25 - b^27)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(5*a^21*b + 30*a^19*b^3 + 61*a^17*b^5 + 8*a^15*b^7 - 182*a^13*b^9 - 364*a^11*b^11 - 350*a^9*b^13 - 184*a^7*b^15 - 47*a^5*b^17 - 2*a^3*b^19 + a*b^21)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 3*sqrt(2)*((a^8*b^3 - 4*a^6*b^5 - 10*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^4 + 2*(3*a^6*b^5 + 5*a^4*b^7 + a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^4*b^7 + 2*a^2*b^9 + b^11)*d + 4*((a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d*cos(d*x + c)^3 + (a^5*b^6 + 2*a^3*b^8 + a*b^10)*d*cos(d*x + c))*sin(d*x + c) - ((a^13*b^3 - 14*a^11*b^5 + 35*a^9*b^7 + 76*a^7*b^9 - 9*a^5*b^11 - 30*a^3*b^13 + 5*a*b^15)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^5 - 25*a^9*b^7 - 34*a^7*b^9 + 14*a^5*b^11 + 15*a^3*b^13 - 5*a*b^15)*d^3*cos(d*x + c)^2 + (a^9*b^7 - 8*a^7*b^9 - 14*a^5*b^11 + 5*a*b^15)*d^3 + 4*((a^12*b^4 - 9*a^10*b^6 - 6*a^8*b^8 + 14*a^6*b^10 + 5*a^4*b^12 - 5*a^2*b^14)*d^3*cos(d*x + c)^3 + (a^10*b^6 - 8*a^8*b^8 - 14*a^6*b^10 + 5*a^2*b^14)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^8*b^3 - 4*a^6*b^5 - 10*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^4 + 2*(3*a^6*b^5 + 5*a^4*b^7 + a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^4*b^7 + 2*a^2*b^9 + b^11)*d + 4*((a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d*cos(d*x + c)^3 + (a^5*b^6 + 2*a^3*b^8 + a*b^10)*d*cos(d*x + c))*sin(d*x + c) - ((a^13*b^3 - 14*a^11*b^5 + 35*a^9*b^7 + 76*a^7*b^9 - 9*a^5*b^11 - 30*a^3*b^13 + 5*a*b^15)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^5 - 25*a^9*b^7 - 34*a^7*b^9 + 14*a^5*b^11 + 15*a^3*b^13 - 5*a*b^15)*d^3*cos(d*x + c)^2 + (a^9*b^7 - 8*a^7*b^9 - 14*a^5*b^11 + 5*a*b^15)*d^3 + 4*((a^12*b^4 - 9*a^10*b^6 - 6*a^8*b^8 + 14*a^6*b^10 + 5*a^4*b^12 - 5*a^2*b^14)*d^3*cos(d*x + c)^3 + (a^10*b^6 - 8*a^8*b^8 - 14*a^6*b^10 + 5*a^2*b^14)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) + 8*(3*a^4*b^4 + 6*a^2*b^6 + 3*b^8 + (8*a^8 - 18*a^6*b^2 - 65*a^4*b^4 - 12*a^2*b^6 + 3*b^8)*cos(d*x + c)^4 + (35*a^6*b^2 + 65*a^4*b^4 + 6*a^2*b^6 - 6*b^8)*cos(d*x + c)^2 + 2*(2*(7*a^7*b + 10*a^5*b^3 - 6*a^3*b^5 - 3*a*b^7)*cos(d*x + c)^3 + 3*(3*a^5*b^3 + 6*a^3*b^5 + 2*a*b^7)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8*b^3 - 4*a^6*b^5 - 10*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^4 + 2*(3*a^6*b^5 + 5*a^4*b^7 + a^2*b^9 - b^11)*d*cos(d*x + c)^2 + (a^4*b^7 + 2*a^2*b^9 + b^11)*d + 4*((a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d*cos(d*x + c)^3 + (a^5*b^6 + 2*a^3*b^8 + a*b^10)*d*cos(d*x + c))*sin(d*x + c))","B",0
548,1,9834,0,2.109153," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left({\left(a^{18} b^{2} + a^{16} b^{4} - 20 \, a^{14} b^{6} - 84 \, a^{12} b^{8} - 154 \, a^{10} b^{10} - 154 \, a^{8} b^{12} - 84 \, a^{6} b^{14} - 20 \, a^{4} b^{16} + a^{2} b^{18} + b^{20}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{4} + 20 \, a^{14} b^{6} + 56 \, a^{12} b^{8} + 84 \, a^{10} b^{10} + 70 \, a^{8} b^{12} + 28 \, a^{6} b^{14} - 4 \, a^{2} b^{18} - b^{20}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{6} + 7 \, a^{12} b^{8} + 21 \, a^{10} b^{10} + 35 \, a^{8} b^{12} + 35 \, a^{6} b^{14} + 21 \, a^{4} b^{16} + 7 \, a^{2} b^{18} + b^{20}\right)} d^{5} + 4 \, {\left({\left(a^{17} b^{3} + 6 \, a^{15} b^{5} + 14 \, a^{13} b^{7} + 14 \, a^{11} b^{9} - 14 \, a^{7} b^{13} - 14 \, a^{5} b^{15} - 6 \, a^{3} b^{17} - a b^{19}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{5} + 7 \, a^{13} b^{7} + 21 \, a^{11} b^{9} + 35 \, a^{9} b^{11} + 35 \, a^{7} b^{13} + 21 \, a^{5} b^{15} + 7 \, a^{3} b^{17} + a b^{19}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{23} + 7 \, a^{21} b^{2} + 15 \, a^{19} b^{4} - 15 \, a^{17} b^{6} - 150 \, a^{15} b^{8} - 378 \, a^{13} b^{10} - 546 \, a^{11} b^{12} - 510 \, a^{9} b^{14} - 315 \, a^{7} b^{16} - 125 \, a^{5} b^{18} - 29 \, a^{3} b^{20} - 3 \, a b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(5 \, a^{27} + 25 \, a^{25} b^{2} + 6 \, a^{23} b^{4} - 218 \, a^{21} b^{6} - 585 \, a^{19} b^{8} - 405 \, a^{17} b^{10} + 900 \, a^{15} b^{12} + 2532 \, a^{13} b^{14} + 2979 \, a^{11} b^{16} + 2015 \, a^{9} b^{18} + 790 \, a^{7} b^{20} + 150 \, a^{5} b^{22} + a^{3} b^{24} - 3 \, a b^{26}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{22} + 25 \, a^{20} b^{2} + 31 \, a^{18} b^{4} - 53 \, a^{16} b^{6} - 190 \, a^{14} b^{8} - 182 \, a^{12} b^{10} + 14 \, a^{10} b^{12} + 166 \, a^{8} b^{14} + 137 \, a^{6} b^{16} + 45 \, a^{4} b^{18} + 3 \, a^{2} b^{20} - b^{22}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 12 \, \sqrt{2} {\left({\left(a^{18} b^{2} + a^{16} b^{4} - 20 \, a^{14} b^{6} - 84 \, a^{12} b^{8} - 154 \, a^{10} b^{10} - 154 \, a^{8} b^{12} - 84 \, a^{6} b^{14} - 20 \, a^{4} b^{16} + a^{2} b^{18} + b^{20}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{4} + 20 \, a^{14} b^{6} + 56 \, a^{12} b^{8} + 84 \, a^{10} b^{10} + 70 \, a^{8} b^{12} + 28 \, a^{6} b^{14} - 4 \, a^{2} b^{18} - b^{20}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{6} + 7 \, a^{12} b^{8} + 21 \, a^{10} b^{10} + 35 \, a^{8} b^{12} + 35 \, a^{6} b^{14} + 21 \, a^{4} b^{16} + 7 \, a^{2} b^{18} + b^{20}\right)} d^{5} + 4 \, {\left({\left(a^{17} b^{3} + 6 \, a^{15} b^{5} + 14 \, a^{13} b^{7} + 14 \, a^{11} b^{9} - 14 \, a^{7} b^{13} - 14 \, a^{5} b^{15} - 6 \, a^{3} b^{17} - a b^{19}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{5} + 7 \, a^{13} b^{7} + 21 \, a^{11} b^{9} + 35 \, a^{9} b^{11} + 35 \, a^{7} b^{13} + 21 \, a^{5} b^{15} + 7 \, a^{3} b^{17} + a b^{19}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{23} + 7 \, a^{21} b^{2} + 15 \, a^{19} b^{4} - 15 \, a^{17} b^{6} - 150 \, a^{15} b^{8} - 378 \, a^{13} b^{10} - 546 \, a^{11} b^{12} - 510 \, a^{9} b^{14} - 315 \, a^{7} b^{16} - 125 \, a^{5} b^{18} - 29 \, a^{3} b^{20} - 3 \, a b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(5 \, a^{27} + 25 \, a^{25} b^{2} + 6 \, a^{23} b^{4} - 218 \, a^{21} b^{6} - 585 \, a^{19} b^{8} - 405 \, a^{17} b^{10} + 900 \, a^{15} b^{12} + 2532 \, a^{13} b^{14} + 2979 \, a^{11} b^{16} + 2015 \, a^{9} b^{18} + 790 \, a^{7} b^{20} + 150 \, a^{5} b^{22} + a^{3} b^{24} - 3 \, a b^{26}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{22} + 25 \, a^{20} b^{2} + 31 \, a^{18} b^{4} - 53 \, a^{16} b^{6} - 190 \, a^{14} b^{8} - 182 \, a^{12} b^{10} + 14 \, a^{10} b^{12} + 166 \, a^{8} b^{14} + 137 \, a^{6} b^{16} + 45 \, a^{4} b^{18} + 3 \, a^{2} b^{20} - b^{22}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} - 10 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{4} + 5 \, a^{4} b^{6} + a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} d + 4 \, {\left({\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{13} b^{2} - 14 \, a^{11} b^{4} + 35 \, a^{9} b^{6} + 76 \, a^{7} b^{8} - 9 \, a^{5} b^{10} - 30 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 34 \, a^{7} b^{8} + 14 \, a^{5} b^{10} + 15 \, a^{3} b^{12} - 5 \, a b^{14}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{6} - 8 \, a^{7} b^{8} - 14 \, a^{5} b^{10} + 5 \, a b^{14}\right)} d^{3} + 4 \, {\left({\left(a^{12} b^{3} - 9 \, a^{10} b^{5} - 6 \, a^{8} b^{7} + 14 \, a^{6} b^{9} + 5 \, a^{4} b^{11} - 5 \, a^{2} b^{13}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{5} - 8 \, a^{8} b^{7} - 14 \, a^{6} b^{9} + 5 \, a^{2} b^{13}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} - 10 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{4} + 5 \, a^{4} b^{6} + a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} d + 4 \, {\left({\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{13} b^{2} - 14 \, a^{11} b^{4} + 35 \, a^{9} b^{6} + 76 \, a^{7} b^{8} - 9 \, a^{5} b^{10} - 30 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 34 \, a^{7} b^{8} + 14 \, a^{5} b^{10} + 15 \, a^{3} b^{12} - 5 \, a b^{14}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{6} - 8 \, a^{7} b^{8} - 14 \, a^{5} b^{10} + 5 \, a b^{14}\right)} d^{3} + 4 \, {\left({\left(a^{12} b^{3} - 9 \, a^{10} b^{5} - 6 \, a^{8} b^{7} + 14 \, a^{6} b^{9} + 5 \, a^{4} b^{11} - 5 \, a^{2} b^{13}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{5} - 8 \, a^{8} b^{7} - 14 \, a^{6} b^{9} + 5 \, a^{2} b^{13}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(2 \, {\left(a^{7} - 13 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{5} b^{2} + 13 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(7 \, a^{6} b + 22 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} - 10 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{4} + 5 \, a^{4} b^{6} + a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} d + 4 \, {\left({\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/12*(12*sqrt(2)*((a^18*b^2 + a^16*b^4 - 20*a^14*b^6 - 84*a^12*b^8 - 154*a^10*b^10 - 154*a^8*b^12 - 84*a^6*b^14 - 20*a^4*b^16 + a^2*b^18 + b^20)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^4 + 20*a^14*b^6 + 56*a^12*b^8 + 84*a^10*b^10 + 70*a^8*b^12 + 28*a^6*b^14 - 4*a^2*b^18 - b^20)*d^5*cos(d*x + c)^2 + (a^14*b^6 + 7*a^12*b^8 + 21*a^10*b^10 + 35*a^8*b^12 + 35*a^6*b^14 + 21*a^4*b^16 + 7*a^2*b^18 + b^20)*d^5 + 4*((a^17*b^3 + 6*a^15*b^5 + 14*a^13*b^7 + 14*a^11*b^9 - 14*a^7*b^13 - 14*a^5*b^15 - 6*a^3*b^17 - a*b^19)*d^5*cos(d*x + c)^3 + (a^15*b^5 + 7*a^13*b^7 + 21*a^11*b^9 + 35*a^9*b^11 + 35*a^7*b^13 + 21*a^5*b^15 + 7*a^3*b^17 + a*b^19)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) - sqrt(2)*((a^23 + 7*a^21*b^2 + 15*a^19*b^4 - 15*a^17*b^6 - 150*a^15*b^8 - 378*a^13*b^10 - 546*a^11*b^12 - 510*a^9*b^14 - 315*a^7*b^16 - 125*a^5*b^18 - 29*a^3*b^20 - 3*a*b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) + sqrt(2)*((5*a^27 + 25*a^25*b^2 + 6*a^23*b^4 - 218*a^21*b^6 - 585*a^19*b^8 - 405*a^17*b^10 + 900*a^15*b^12 + 2532*a^13*b^14 + 2979*a^11*b^16 + 2015*a^9*b^18 + 790*a^7*b^20 + 150*a^5*b^22 + a^3*b^24 - 3*a*b^26)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^22 + 25*a^20*b^2 + 31*a^18*b^4 - 53*a^16*b^6 - 190*a^14*b^8 - 182*a^12*b^10 + 14*a^10*b^12 + 166*a^8*b^14 + 137*a^6*b^16 + 45*a^4*b^18 + 3*a^2*b^20 - b^22)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 12*sqrt(2)*((a^18*b^2 + a^16*b^4 - 20*a^14*b^6 - 84*a^12*b^8 - 154*a^10*b^10 - 154*a^8*b^12 - 84*a^6*b^14 - 20*a^4*b^16 + a^2*b^18 + b^20)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^4 + 20*a^14*b^6 + 56*a^12*b^8 + 84*a^10*b^10 + 70*a^8*b^12 + 28*a^6*b^14 - 4*a^2*b^18 - b^20)*d^5*cos(d*x + c)^2 + (a^14*b^6 + 7*a^12*b^8 + 21*a^10*b^10 + 35*a^8*b^12 + 35*a^6*b^14 + 21*a^4*b^16 + 7*a^2*b^18 + b^20)*d^5 + 4*((a^17*b^3 + 6*a^15*b^5 + 14*a^13*b^7 + 14*a^11*b^9 - 14*a^7*b^13 - 14*a^5*b^15 - 6*a^3*b^17 - a*b^19)*d^5*cos(d*x + c)^3 + (a^15*b^5 + 7*a^13*b^7 + 21*a^11*b^9 + 35*a^9*b^11 + 35*a^7*b^13 + 21*a^5*b^15 + 7*a^3*b^17 + a*b^19)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(-((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) + sqrt(2)*((a^23 + 7*a^21*b^2 + 15*a^19*b^4 - 15*a^17*b^6 - 150*a^15*b^8 - 378*a^13*b^10 - 546*a^11*b^12 - 510*a^9*b^14 - 315*a^7*b^16 - 125*a^5*b^18 - 29*a^3*b^20 - 3*a*b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) - sqrt(2)*((5*a^27 + 25*a^25*b^2 + 6*a^23*b^4 - 218*a^21*b^6 - 585*a^19*b^8 - 405*a^17*b^10 + 900*a^15*b^12 + 2532*a^13*b^14 + 2979*a^11*b^16 + 2015*a^9*b^18 + 790*a^7*b^20 + 150*a^5*b^22 + a^3*b^24 - 3*a*b^26)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^22 + 25*a^20*b^2 + 31*a^18*b^4 - 53*a^16*b^6 - 190*a^14*b^8 - 182*a^12*b^10 + 14*a^10*b^12 + 166*a^8*b^14 + 137*a^6*b^16 + 45*a^4*b^18 + 3*a^2*b^20 - b^22)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) - 3*sqrt(2)*((a^8*b^2 - 4*a^6*b^4 - 10*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^4 + 2*(3*a^6*b^4 + 5*a^4*b^6 + a^2*b^8 - b^10)*d*cos(d*x + c)^2 + (a^4*b^6 + 2*a^2*b^8 + b^10)*d + 4*((a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d*cos(d*x + c)^3 + (a^5*b^5 + 2*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sin(d*x + c) + ((a^13*b^2 - 14*a^11*b^4 + 35*a^9*b^6 + 76*a^7*b^8 - 9*a^5*b^10 - 30*a^3*b^12 + 5*a*b^14)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^4 - 25*a^9*b^6 - 34*a^7*b^8 + 14*a^5*b^10 + 15*a^3*b^12 - 5*a*b^14)*d^3*cos(d*x + c)^2 + (a^9*b^6 - 8*a^7*b^8 - 14*a^5*b^10 + 5*a*b^14)*d^3 + 4*((a^12*b^3 - 9*a^10*b^5 - 6*a^8*b^7 + 14*a^6*b^9 + 5*a^4*b^11 - 5*a^2*b^13)*d^3*cos(d*x + c)^3 + (a^10*b^5 - 8*a^8*b^7 - 14*a^6*b^9 + 5*a^2*b^13)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^8*b^2 - 4*a^6*b^4 - 10*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^4 + 2*(3*a^6*b^4 + 5*a^4*b^6 + a^2*b^8 - b^10)*d*cos(d*x + c)^2 + (a^4*b^6 + 2*a^2*b^8 + b^10)*d + 4*((a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d*cos(d*x + c)^3 + (a^5*b^5 + 2*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sin(d*x + c) + ((a^13*b^2 - 14*a^11*b^4 + 35*a^9*b^6 + 76*a^7*b^8 - 9*a^5*b^10 - 30*a^3*b^12 + 5*a*b^14)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^4 - 25*a^9*b^6 - 34*a^7*b^8 + 14*a^5*b^10 + 15*a^3*b^12 - 5*a*b^14)*d^3*cos(d*x + c)^2 + (a^9*b^6 - 8*a^7*b^8 - 14*a^5*b^10 + 5*a*b^14)*d^3 + 4*((a^12*b^3 - 9*a^10*b^5 - 6*a^8*b^7 + 14*a^6*b^9 + 5*a^4*b^11 - 5*a^2*b^13)*d^3*cos(d*x + c)^3 + (a^10*b^5 - 8*a^8*b^7 - 14*a^6*b^9 + 5*a^2*b^13)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c)) + 8*(2*(a^7 - 13*a^3*b^4)*cos(d*x + c)^4 + 2*(4*a^5*b^2 + 13*a^3*b^4)*cos(d*x + c)^2 + ((7*a^6*b + 22*a^4*b^3 - 9*a^2*b^5)*cos(d*x + c)^3 + 3*(a^4*b^3 + 3*a^2*b^5)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8*b^2 - 4*a^6*b^4 - 10*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^4 + 2*(3*a^6*b^4 + 5*a^4*b^6 + a^2*b^8 - b^10)*d*cos(d*x + c)^2 + (a^4*b^6 + 2*a^2*b^8 + b^10)*d + 4*((a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d*cos(d*x + c)^3 + (a^5*b^5 + 2*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sin(d*x + c))","B",0
549,1,9804,0,2.553423," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left({\left(a^{18} b + a^{16} b^{3} - 20 \, a^{14} b^{5} - 84 \, a^{12} b^{7} - 154 \, a^{10} b^{9} - 154 \, a^{8} b^{11} - 84 \, a^{6} b^{13} - 20 \, a^{4} b^{15} + a^{2} b^{17} + b^{19}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{3} + 20 \, a^{14} b^{5} + 56 \, a^{12} b^{7} + 84 \, a^{10} b^{9} + 70 \, a^{8} b^{11} + 28 \, a^{6} b^{13} - 4 \, a^{2} b^{17} - b^{19}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{5} + 7 \, a^{12} b^{7} + 21 \, a^{10} b^{9} + 35 \, a^{8} b^{11} + 35 \, a^{6} b^{13} + 21 \, a^{4} b^{15} + 7 \, a^{2} b^{17} + b^{19}\right)} d^{5} + 4 \, {\left({\left(a^{17} b^{2} + 6 \, a^{15} b^{4} + 14 \, a^{13} b^{6} + 14 \, a^{11} b^{8} - 14 \, a^{7} b^{12} - 14 \, a^{5} b^{14} - 6 \, a^{3} b^{16} - a b^{18}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{4} + 7 \, a^{13} b^{6} + 21 \, a^{11} b^{8} + 35 \, a^{9} b^{10} + 35 \, a^{7} b^{12} + 21 \, a^{5} b^{14} + 7 \, a^{3} b^{16} + a b^{18}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{22} + 29 \, a^{20} b^{2} + 125 \, a^{18} b^{4} + 315 \, a^{16} b^{6} + 510 \, a^{14} b^{8} + 546 \, a^{12} b^{10} + 378 \, a^{10} b^{12} + 150 \, a^{8} b^{14} + 15 \, a^{6} b^{16} - 15 \, a^{4} b^{18} - 7 \, a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(a^{17} + 8 \, a^{15} b^{2} + 28 \, a^{13} b^{4} + 56 \, a^{11} b^{6} + 70 \, a^{9} b^{8} + 56 \, a^{7} b^{10} + 28 \, a^{5} b^{12} + 8 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(15 \, a^{26} b + 115 \, a^{24} b^{3} + 338 \, a^{22} b^{5} + 354 \, a^{20} b^{7} - 475 \, a^{18} b^{9} - 2055 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} - 2484 \, a^{12} b^{15} - 1047 \, a^{10} b^{17} - 75 \, a^{8} b^{19} + 130 \, a^{6} b^{21} + 50 \, a^{4} b^{23} + 3 \, a^{2} b^{25} - b^{27}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(5 \, a^{21} b + 30 \, a^{19} b^{3} + 61 \, a^{17} b^{5} + 8 \, a^{15} b^{7} - 182 \, a^{13} b^{9} - 364 \, a^{11} b^{11} - 350 \, a^{9} b^{13} - 184 \, a^{7} b^{15} - 47 \, a^{5} b^{17} - 2 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 12 \, \sqrt{2} {\left({\left(a^{18} b + a^{16} b^{3} - 20 \, a^{14} b^{5} - 84 \, a^{12} b^{7} - 154 \, a^{10} b^{9} - 154 \, a^{8} b^{11} - 84 \, a^{6} b^{13} - 20 \, a^{4} b^{15} + a^{2} b^{17} + b^{19}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{3} + 20 \, a^{14} b^{5} + 56 \, a^{12} b^{7} + 84 \, a^{10} b^{9} + 70 \, a^{8} b^{11} + 28 \, a^{6} b^{13} - 4 \, a^{2} b^{17} - b^{19}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{5} + 7 \, a^{12} b^{7} + 21 \, a^{10} b^{9} + 35 \, a^{8} b^{11} + 35 \, a^{6} b^{13} + 21 \, a^{4} b^{15} + 7 \, a^{2} b^{17} + b^{19}\right)} d^{5} + 4 \, {\left({\left(a^{17} b^{2} + 6 \, a^{15} b^{4} + 14 \, a^{13} b^{6} + 14 \, a^{11} b^{8} - 14 \, a^{7} b^{12} - 14 \, a^{5} b^{14} - 6 \, a^{3} b^{16} - a b^{18}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{4} + 7 \, a^{13} b^{6} + 21 \, a^{11} b^{8} + 35 \, a^{9} b^{10} + 35 \, a^{7} b^{12} + 21 \, a^{5} b^{14} + 7 \, a^{3} b^{16} + a b^{18}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{22} + 29 \, a^{20} b^{2} + 125 \, a^{18} b^{4} + 315 \, a^{16} b^{6} + 510 \, a^{14} b^{8} + 546 \, a^{12} b^{10} + 378 \, a^{10} b^{12} + 150 \, a^{8} b^{14} + 15 \, a^{6} b^{16} - 15 \, a^{4} b^{18} - 7 \, a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(a^{17} + 8 \, a^{15} b^{2} + 28 \, a^{13} b^{4} + 56 \, a^{11} b^{6} + 70 \, a^{9} b^{8} + 56 \, a^{7} b^{10} + 28 \, a^{5} b^{12} + 8 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(15 \, a^{26} b + 115 \, a^{24} b^{3} + 338 \, a^{22} b^{5} + 354 \, a^{20} b^{7} - 475 \, a^{18} b^{9} - 2055 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} - 2484 \, a^{12} b^{15} - 1047 \, a^{10} b^{17} - 75 \, a^{8} b^{19} + 130 \, a^{6} b^{21} + 50 \, a^{4} b^{23} + 3 \, a^{2} b^{25} - b^{27}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(5 \, a^{21} b + 30 \, a^{19} b^{3} + 61 \, a^{17} b^{5} + 8 \, a^{15} b^{7} - 182 \, a^{13} b^{9} - 364 \, a^{11} b^{11} - 350 \, a^{9} b^{13} - 184 \, a^{7} b^{15} - 47 \, a^{5} b^{17} - 2 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} b - 4 \, a^{6} b^{3} - 10 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d + 4 \, {\left({\left(a^{7} b^{2} + a^{5} b^{4} - a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{13} b - 14 \, a^{11} b^{3} + 35 \, a^{9} b^{5} + 76 \, a^{7} b^{7} - 9 \, a^{5} b^{9} - 30 \, a^{3} b^{11} + 5 \, a b^{13}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{3} - 25 \, a^{9} b^{5} - 34 \, a^{7} b^{7} + 14 \, a^{5} b^{9} + 15 \, a^{3} b^{11} - 5 \, a b^{13}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{5} - 8 \, a^{7} b^{7} - 14 \, a^{5} b^{9} + 5 \, a b^{13}\right)} d^{3} + 4 \, {\left({\left(a^{12} b^{2} - 9 \, a^{10} b^{4} - 6 \, a^{8} b^{6} + 14 \, a^{6} b^{8} + 5 \, a^{4} b^{10} - 5 \, a^{2} b^{12}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{4} - 8 \, a^{8} b^{6} - 14 \, a^{6} b^{8} + 5 \, a^{2} b^{12}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} b - 4 \, a^{6} b^{3} - 10 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d + 4 \, {\left({\left(a^{7} b^{2} + a^{5} b^{4} - a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{13} b - 14 \, a^{11} b^{3} + 35 \, a^{9} b^{5} + 76 \, a^{7} b^{7} - 9 \, a^{5} b^{9} - 30 \, a^{3} b^{11} + 5 \, a b^{13}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{3} - 25 \, a^{9} b^{5} - 34 \, a^{7} b^{7} + 14 \, a^{5} b^{9} + 15 \, a^{3} b^{11} - 5 \, a b^{13}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{5} - 8 \, a^{7} b^{7} - 14 \, a^{5} b^{9} + 5 \, a b^{13}\right)} d^{3} + 4 \, {\left({\left(a^{12} b^{2} - 9 \, a^{10} b^{4} - 6 \, a^{8} b^{6} + 14 \, a^{6} b^{8} + 5 \, a^{4} b^{10} - 5 \, a^{2} b^{12}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{4} - 8 \, a^{8} b^{6} - 14 \, a^{6} b^{8} + 5 \, a^{2} b^{12}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left({\left(a^{6} - 6 \, a^{4} b^{2} + 17 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{4} b^{2} - 17 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(3 \, a b^{5} \cos\left(d x + c\right) - {\left(a^{5} b - 8 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} b - 4 \, a^{6} b^{3} - 10 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d + 4 \, {\left({\left(a^{7} b^{2} + a^{5} b^{4} - a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/12*(12*sqrt(2)*((a^18*b + a^16*b^3 - 20*a^14*b^5 - 84*a^12*b^7 - 154*a^10*b^9 - 154*a^8*b^11 - 84*a^6*b^13 - 20*a^4*b^15 + a^2*b^17 + b^19)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^3 + 20*a^14*b^5 + 56*a^12*b^7 + 84*a^10*b^9 + 70*a^8*b^11 + 28*a^6*b^13 - 4*a^2*b^17 - b^19)*d^5*cos(d*x + c)^2 + (a^14*b^5 + 7*a^12*b^7 + 21*a^10*b^9 + 35*a^8*b^11 + 35*a^6*b^13 + 21*a^4*b^15 + 7*a^2*b^17 + b^19)*d^5 + 4*((a^17*b^2 + 6*a^15*b^4 + 14*a^13*b^6 + 14*a^11*b^8 - 14*a^7*b^12 - 14*a^5*b^14 - 6*a^3*b^16 - a*b^18)*d^5*cos(d*x + c)^3 + (a^15*b^4 + 7*a^13*b^6 + 21*a^11*b^8 + 35*a^9*b^10 + 35*a^7*b^12 + 21*a^5*b^14 + 7*a^3*b^16 + a*b^18)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) - sqrt(2)*((3*a^22 + 29*a^20*b^2 + 125*a^18*b^4 + 315*a^16*b^6 + 510*a^14*b^8 + 546*a^12*b^10 + 378*a^10*b^12 + 150*a^8*b^14 + 15*a^6*b^16 - 15*a^4*b^18 - 7*a^2*b^20 - b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(a^17 + 8*a^15*b^2 + 28*a^13*b^4 + 56*a^11*b^6 + 70*a^9*b^8 + 56*a^7*b^10 + 28*a^5*b^12 + 8*a^3*b^14 + a*b^16)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) + sqrt(2)*((15*a^26*b + 115*a^24*b^3 + 338*a^22*b^5 + 354*a^20*b^7 - 475*a^18*b^9 - 2055*a^16*b^11 - 3060*a^14*b^13 - 2484*a^12*b^15 - 1047*a^10*b^17 - 75*a^8*b^19 + 130*a^6*b^21 + 50*a^4*b^23 + 3*a^2*b^25 - b^27)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(5*a^21*b + 30*a^19*b^3 + 61*a^17*b^5 + 8*a^15*b^7 - 182*a^13*b^9 - 364*a^11*b^11 - 350*a^9*b^13 - 184*a^7*b^15 - 47*a^5*b^17 - 2*a^3*b^19 + a*b^21)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 12*sqrt(2)*((a^18*b + a^16*b^3 - 20*a^14*b^5 - 84*a^12*b^7 - 154*a^10*b^9 - 154*a^8*b^11 - 84*a^6*b^13 - 20*a^4*b^15 + a^2*b^17 + b^19)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^3 + 20*a^14*b^5 + 56*a^12*b^7 + 84*a^10*b^9 + 70*a^8*b^11 + 28*a^6*b^13 - 4*a^2*b^17 - b^19)*d^5*cos(d*x + c)^2 + (a^14*b^5 + 7*a^12*b^7 + 21*a^10*b^9 + 35*a^8*b^11 + 35*a^6*b^13 + 21*a^4*b^15 + 7*a^2*b^17 + b^19)*d^5 + 4*((a^17*b^2 + 6*a^15*b^4 + 14*a^13*b^6 + 14*a^11*b^8 - 14*a^7*b^12 - 14*a^5*b^14 - 6*a^3*b^16 - a*b^18)*d^5*cos(d*x + c)^3 + (a^15*b^4 + 7*a^13*b^6 + 21*a^11*b^8 + 35*a^9*b^10 + 35*a^7*b^12 + 21*a^5*b^14 + 7*a^3*b^16 + a*b^18)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(-((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) + sqrt(2)*((3*a^22 + 29*a^20*b^2 + 125*a^18*b^4 + 315*a^16*b^6 + 510*a^14*b^8 + 546*a^12*b^10 + 378*a^10*b^12 + 150*a^8*b^14 + 15*a^6*b^16 - 15*a^4*b^18 - 7*a^2*b^20 - b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(a^17 + 8*a^15*b^2 + 28*a^13*b^4 + 56*a^11*b^6 + 70*a^9*b^8 + 56*a^7*b^10 + 28*a^5*b^12 + 8*a^3*b^14 + a*b^16)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) - sqrt(2)*((15*a^26*b + 115*a^24*b^3 + 338*a^22*b^5 + 354*a^20*b^7 - 475*a^18*b^9 - 2055*a^16*b^11 - 3060*a^14*b^13 - 2484*a^12*b^15 - 1047*a^10*b^17 - 75*a^8*b^19 + 130*a^6*b^21 + 50*a^4*b^23 + 3*a^2*b^25 - b^27)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(5*a^21*b + 30*a^19*b^3 + 61*a^17*b^5 + 8*a^15*b^7 - 182*a^13*b^9 - 364*a^11*b^11 - 350*a^9*b^13 - 184*a^7*b^15 - 47*a^5*b^17 - 2*a^3*b^19 + a*b^21)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 3*sqrt(2)*((a^8*b - 4*a^6*b^3 - 10*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^4 + 2*(3*a^6*b^3 + 5*a^4*b^5 + a^2*b^7 - b^9)*d*cos(d*x + c)^2 + (a^4*b^5 + 2*a^2*b^7 + b^9)*d + 4*((a^7*b^2 + a^5*b^4 - a^3*b^6 - a*b^8)*d*cos(d*x + c)^3 + (a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sin(d*x + c) - ((a^13*b - 14*a^11*b^3 + 35*a^9*b^5 + 76*a^7*b^7 - 9*a^5*b^9 - 30*a^3*b^11 + 5*a*b^13)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^3 - 25*a^9*b^5 - 34*a^7*b^7 + 14*a^5*b^9 + 15*a^3*b^11 - 5*a*b^13)*d^3*cos(d*x + c)^2 + (a^9*b^5 - 8*a^7*b^7 - 14*a^5*b^9 + 5*a*b^13)*d^3 + 4*((a^12*b^2 - 9*a^10*b^4 - 6*a^8*b^6 + 14*a^6*b^8 + 5*a^4*b^10 - 5*a^2*b^12)*d^3*cos(d*x + c)^3 + (a^10*b^4 - 8*a^8*b^6 - 14*a^6*b^8 + 5*a^2*b^12)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^8*b - 4*a^6*b^3 - 10*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^4 + 2*(3*a^6*b^3 + 5*a^4*b^5 + a^2*b^7 - b^9)*d*cos(d*x + c)^2 + (a^4*b^5 + 2*a^2*b^7 + b^9)*d + 4*((a^7*b^2 + a^5*b^4 - a^3*b^6 - a*b^8)*d*cos(d*x + c)^3 + (a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sin(d*x + c) - ((a^13*b - 14*a^11*b^3 + 35*a^9*b^5 + 76*a^7*b^7 - 9*a^5*b^9 - 30*a^3*b^11 + 5*a*b^13)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^3 - 25*a^9*b^5 - 34*a^7*b^7 + 14*a^5*b^9 + 15*a^3*b^11 - 5*a*b^13)*d^3*cos(d*x + c)^2 + (a^9*b^5 - 8*a^7*b^7 - 14*a^5*b^9 + 5*a*b^13)*d^3 + 4*((a^12*b^2 - 9*a^10*b^4 - 6*a^8*b^6 + 14*a^6*b^8 + 5*a^4*b^10 - 5*a^2*b^12)*d^3*cos(d*x + c)^3 + (a^10*b^4 - 8*a^8*b^6 - 14*a^6*b^8 + 5*a^2*b^12)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) + 8*((a^6 - 6*a^4*b^2 + 17*a^2*b^4)*cos(d*x + c)^4 + (a^4*b^2 - 17*a^2*b^4)*cos(d*x + c)^2 - 2*(3*a*b^5*cos(d*x + c) - (a^5*b - 8*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8*b - 4*a^6*b^3 - 10*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^4 + 2*(3*a^6*b^3 + 5*a^4*b^5 + a^2*b^7 - b^9)*d*cos(d*x + c)^2 + (a^4*b^5 + 2*a^2*b^7 + b^9)*d + 4*((a^7*b^2 + a^5*b^4 - a^3*b^6 - a*b^8)*d*cos(d*x + c)^3 + (a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c))*sin(d*x + c))","B",0
550,1,9790,0,3.011068," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(a^{18} + a^{16} b^{2} - 20 \, a^{14} b^{4} - 84 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 154 \, a^{8} b^{10} - 84 \, a^{6} b^{12} - 20 \, a^{4} b^{14} + a^{2} b^{16} + b^{18}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 56 \, a^{12} b^{6} + 84 \, a^{10} b^{8} + 70 \, a^{8} b^{10} + 28 \, a^{6} b^{12} - 4 \, a^{2} b^{16} - b^{18}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{4} + 7 \, a^{12} b^{6} + 21 \, a^{10} b^{8} + 35 \, a^{8} b^{10} + 35 \, a^{6} b^{12} + 21 \, a^{4} b^{14} + 7 \, a^{2} b^{16} + b^{18}\right)} d^{5} + 4 \, {\left({\left(a^{17} b + 6 \, a^{15} b^{3} + 14 \, a^{13} b^{5} + 14 \, a^{11} b^{7} - 14 \, a^{7} b^{11} - 14 \, a^{5} b^{13} - 6 \, a^{3} b^{15} - a b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{3} + 7 \, a^{13} b^{5} + 21 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 35 \, a^{7} b^{11} + 21 \, a^{5} b^{13} + 7 \, a^{3} b^{15} + a b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{23} + 7 \, a^{21} b^{2} + 15 \, a^{19} b^{4} - 15 \, a^{17} b^{6} - 150 \, a^{15} b^{8} - 378 \, a^{13} b^{10} - 546 \, a^{11} b^{12} - 510 \, a^{9} b^{14} - 315 \, a^{7} b^{16} - 125 \, a^{5} b^{18} - 29 \, a^{3} b^{20} - 3 \, a b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(5 \, a^{27} + 25 \, a^{25} b^{2} + 6 \, a^{23} b^{4} - 218 \, a^{21} b^{6} - 585 \, a^{19} b^{8} - 405 \, a^{17} b^{10} + 900 \, a^{15} b^{12} + 2532 \, a^{13} b^{14} + 2979 \, a^{11} b^{16} + 2015 \, a^{9} b^{18} + 790 \, a^{7} b^{20} + 150 \, a^{5} b^{22} + a^{3} b^{24} - 3 \, a b^{26}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{22} + 25 \, a^{20} b^{2} + 31 \, a^{18} b^{4} - 53 \, a^{16} b^{6} - 190 \, a^{14} b^{8} - 182 \, a^{12} b^{10} + 14 \, a^{10} b^{12} + 166 \, a^{8} b^{14} + 137 \, a^{6} b^{16} + 45 \, a^{4} b^{18} + 3 \, a^{2} b^{20} - b^{22}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 12 \, \sqrt{2} {\left({\left(a^{18} + a^{16} b^{2} - 20 \, a^{14} b^{4} - 84 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 154 \, a^{8} b^{10} - 84 \, a^{6} b^{12} - 20 \, a^{4} b^{14} + a^{2} b^{16} + b^{18}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 56 \, a^{12} b^{6} + 84 \, a^{10} b^{8} + 70 \, a^{8} b^{10} + 28 \, a^{6} b^{12} - 4 \, a^{2} b^{16} - b^{18}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{4} + 7 \, a^{12} b^{6} + 21 \, a^{10} b^{8} + 35 \, a^{8} b^{10} + 35 \, a^{6} b^{12} + 21 \, a^{4} b^{14} + 7 \, a^{2} b^{16} + b^{18}\right)} d^{5} + 4 \, {\left({\left(a^{17} b + 6 \, a^{15} b^{3} + 14 \, a^{13} b^{5} + 14 \, a^{11} b^{7} - 14 \, a^{7} b^{11} - 14 \, a^{5} b^{13} - 6 \, a^{3} b^{15} - a b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{3} + 7 \, a^{13} b^{5} + 21 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 35 \, a^{7} b^{11} + 21 \, a^{5} b^{13} + 7 \, a^{3} b^{15} + a b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{23} + 7 \, a^{21} b^{2} + 15 \, a^{19} b^{4} - 15 \, a^{17} b^{6} - 150 \, a^{15} b^{8} - 378 \, a^{13} b^{10} - 546 \, a^{11} b^{12} - 510 \, a^{9} b^{14} - 315 \, a^{7} b^{16} - 125 \, a^{5} b^{18} - 29 \, a^{3} b^{20} - 3 \, a b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(5 \, a^{27} + 25 \, a^{25} b^{2} + 6 \, a^{23} b^{4} - 218 \, a^{21} b^{6} - 585 \, a^{19} b^{8} - 405 \, a^{17} b^{10} + 900 \, a^{15} b^{12} + 2532 \, a^{13} b^{14} + 2979 \, a^{11} b^{16} + 2015 \, a^{9} b^{18} + 790 \, a^{7} b^{20} + 150 \, a^{5} b^{22} + a^{3} b^{24} - 3 \, a b^{26}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{22} + 25 \, a^{20} b^{2} + 31 \, a^{18} b^{4} - 53 \, a^{16} b^{6} - 190 \, a^{14} b^{8} - 182 \, a^{12} b^{10} + 14 \, a^{10} b^{12} + 166 \, a^{8} b^{14} + 137 \, a^{6} b^{16} + 45 \, a^{4} b^{18} + 3 \, a^{2} b^{20} - b^{22}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} - 4 \, a^{6} b^{2} - 10 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{13} - 14 \, a^{11} b^{2} + 35 \, a^{9} b^{4} + 76 \, a^{7} b^{6} - 9 \, a^{5} b^{8} - 30 \, a^{3} b^{10} + 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{2} - 25 \, a^{9} b^{4} - 34 \, a^{7} b^{6} + 14 \, a^{5} b^{8} + 15 \, a^{3} b^{10} - 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{4} - 8 \, a^{7} b^{6} - 14 \, a^{5} b^{8} + 5 \, a b^{12}\right)} d^{3} + 4 \, {\left({\left(a^{12} b - 9 \, a^{10} b^{3} - 6 \, a^{8} b^{5} + 14 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{3} - 8 \, a^{8} b^{5} - 14 \, a^{6} b^{7} + 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} - 4 \, a^{6} b^{2} - 10 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + {\left({\left(a^{13} - 14 \, a^{11} b^{2} + 35 \, a^{9} b^{4} + 76 \, a^{7} b^{6} - 9 \, a^{5} b^{8} - 30 \, a^{3} b^{10} + 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{2} - 25 \, a^{9} b^{4} - 34 \, a^{7} b^{6} + 14 \, a^{5} b^{8} + 15 \, a^{3} b^{10} - 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{4} - 8 \, a^{7} b^{6} - 14 \, a^{5} b^{8} + 5 \, a b^{12}\right)} d^{3} + 4 \, {\left({\left(a^{12} b - 9 \, a^{10} b^{3} - 6 \, a^{8} b^{5} + 14 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{3} - 8 \, a^{8} b^{5} - 14 \, a^{6} b^{7} + 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} - 25 \, a^{12} b^{2} - 115 \, a^{10} b^{4} + 35 \, a^{8} b^{6} + 171 \, a^{6} b^{8} + 53 \, a^{4} b^{10} - 17 \, a^{2} b^{12} + b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(25 \, a^{16} - 50 \, a^{14} b^{2} - 90 \, a^{12} b^{4} + 150 \, a^{10} b^{6} + 136 \, a^{8} b^{8} - 118 \, a^{6} b^{10} - 70 \, a^{4} b^{12} + 18 \, a^{2} b^{14} - b^{16}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(25 \, a^{11} - 175 \, a^{9} b^{2} + 410 \, a^{7} b^{4} - 350 \, a^{5} b^{6} + 61 \, a^{3} b^{8} - 3 \, a b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} - {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} - 100 \, a^{7} b^{2} + 110 \, a^{5} b^{4} - 20 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b - 100 \, a^{6} b^{3} + 110 \, a^{4} b^{5} - 20 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(11 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} - 4 \, a^{6} b^{2} - 10 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(12*sqrt(2)*((a^18 + a^16*b^2 - 20*a^14*b^4 - 84*a^12*b^6 - 154*a^10*b^8 - 154*a^8*b^10 - 84*a^6*b^12 - 20*a^4*b^14 + a^2*b^16 + b^18)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^2 + 20*a^14*b^4 + 56*a^12*b^6 + 84*a^10*b^8 + 70*a^8*b^10 + 28*a^6*b^12 - 4*a^2*b^16 - b^18)*d^5*cos(d*x + c)^2 + (a^14*b^4 + 7*a^12*b^6 + 21*a^10*b^8 + 35*a^8*b^10 + 35*a^6*b^12 + 21*a^4*b^14 + 7*a^2*b^16 + b^18)*d^5 + 4*((a^17*b + 6*a^15*b^3 + 14*a^13*b^5 + 14*a^11*b^7 - 14*a^7*b^11 - 14*a^5*b^13 - 6*a^3*b^15 - a*b^17)*d^5*cos(d*x + c)^3 + (a^15*b^3 + 7*a^13*b^5 + 21*a^11*b^7 + 35*a^9*b^9 + 35*a^7*b^11 + 21*a^5*b^13 + 7*a^3*b^15 + a*b^17)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) - sqrt(2)*((a^23 + 7*a^21*b^2 + 15*a^19*b^4 - 15*a^17*b^6 - 150*a^15*b^8 - 378*a^13*b^10 - 546*a^11*b^12 - 510*a^9*b^14 - 315*a^7*b^16 - 125*a^5*b^18 - 29*a^3*b^20 - 3*a*b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) + sqrt(2)*((5*a^27 + 25*a^25*b^2 + 6*a^23*b^4 - 218*a^21*b^6 - 585*a^19*b^8 - 405*a^17*b^10 + 900*a^15*b^12 + 2532*a^13*b^14 + 2979*a^11*b^16 + 2015*a^9*b^18 + 790*a^7*b^20 + 150*a^5*b^22 + a^3*b^24 - 3*a*b^26)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^22 + 25*a^20*b^2 + 31*a^18*b^4 - 53*a^16*b^6 - 190*a^14*b^8 - 182*a^12*b^10 + 14*a^10*b^12 + 166*a^8*b^14 + 137*a^6*b^16 + 45*a^4*b^18 + 3*a^2*b^20 - b^22)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 12*sqrt(2)*((a^18 + a^16*b^2 - 20*a^14*b^4 - 84*a^12*b^6 - 154*a^10*b^8 - 154*a^8*b^10 - 84*a^6*b^12 - 20*a^4*b^14 + a^2*b^16 + b^18)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^2 + 20*a^14*b^4 + 56*a^12*b^6 + 84*a^10*b^8 + 70*a^8*b^10 + 28*a^6*b^12 - 4*a^2*b^16 - b^18)*d^5*cos(d*x + c)^2 + (a^14*b^4 + 7*a^12*b^6 + 21*a^10*b^8 + 35*a^8*b^10 + 35*a^6*b^12 + 21*a^4*b^14 + 7*a^2*b^16 + b^18)*d^5 + 4*((a^17*b + 6*a^15*b^3 + 14*a^13*b^5 + 14*a^11*b^7 - 14*a^7*b^11 - 14*a^5*b^13 - 6*a^3*b^15 - a*b^17)*d^5*cos(d*x + c)^3 + (a^15*b^3 + 7*a^13*b^5 + 21*a^11*b^7 + 35*a^9*b^9 + 35*a^7*b^11 + 21*a^5*b^13 + 7*a^3*b^15 + a*b^17)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(-((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) + sqrt(2)*((a^23 + 7*a^21*b^2 + 15*a^19*b^4 - 15*a^17*b^6 - 150*a^15*b^8 - 378*a^13*b^10 - 546*a^11*b^12 - 510*a^9*b^14 - 315*a^7*b^16 - 125*a^5*b^18 - 29*a^3*b^20 - 3*a*b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) - sqrt(2)*((5*a^27 + 25*a^25*b^2 + 6*a^23*b^4 - 218*a^21*b^6 - 585*a^19*b^8 - 405*a^17*b^10 + 900*a^15*b^12 + 2532*a^13*b^14 + 2979*a^11*b^16 + 2015*a^9*b^18 + 790*a^7*b^20 + 150*a^5*b^22 + a^3*b^24 - 3*a*b^26)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^22 + 25*a^20*b^2 + 31*a^18*b^4 - 53*a^16*b^6 - 190*a^14*b^8 - 182*a^12*b^10 + 14*a^10*b^12 + 166*a^8*b^14 + 137*a^6*b^16 + 45*a^4*b^18 + 3*a^2*b^20 - b^22)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) - 3*sqrt(2)*((a^8 - 4*a^6*b^2 - 10*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + 2*(3*a^6*b^2 + 5*a^4*b^4 + a^2*b^6 - b^8)*d*cos(d*x + c)^2 + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*d*cos(d*x + c)^3 + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sin(d*x + c) + ((a^13 - 14*a^11*b^2 + 35*a^9*b^4 + 76*a^7*b^6 - 9*a^5*b^8 - 30*a^3*b^10 + 5*a*b^12)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^2 - 25*a^9*b^4 - 34*a^7*b^6 + 14*a^5*b^8 + 15*a^3*b^10 - 5*a*b^12)*d^3*cos(d*x + c)^2 + (a^9*b^4 - 8*a^7*b^6 - 14*a^5*b^8 + 5*a*b^12)*d^3 + 4*((a^12*b - 9*a^10*b^3 - 6*a^8*b^5 + 14*a^6*b^7 + 5*a^4*b^9 - 5*a^2*b^11)*d^3*cos(d*x + c)^3 + (a^10*b^3 - 8*a^8*b^5 - 14*a^6*b^7 + 5*a^2*b^11)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^8 - 4*a^6*b^2 - 10*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + 2*(3*a^6*b^2 + 5*a^4*b^4 + a^2*b^6 - b^8)*d*cos(d*x + c)^2 + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*d*cos(d*x + c)^3 + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sin(d*x + c) + ((a^13 - 14*a^11*b^2 + 35*a^9*b^4 + 76*a^7*b^6 - 9*a^5*b^8 - 30*a^3*b^10 + 5*a*b^12)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^2 - 25*a^9*b^4 - 34*a^7*b^6 + 14*a^5*b^8 + 15*a^3*b^10 - 5*a*b^12)*d^3*cos(d*x + c)^2 + (a^9*b^4 - 8*a^7*b^6 - 14*a^5*b^8 + 5*a*b^12)*d^3 + 4*((a^12*b - 9*a^10*b^3 - 6*a^8*b^5 + 14*a^6*b^7 + 5*a^4*b^9 - 5*a^2*b^11)*d^3*cos(d*x + c)^3 + (a^10*b^3 - 8*a^8*b^5 - 14*a^6*b^7 + 5*a^2*b^11)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14 - 25*a^12*b^2 - 115*a^10*b^4 + 35*a^8*b^6 + 171*a^6*b^8 + 53*a^4*b^10 - 17*a^2*b^12 + b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*((25*a^16 - 50*a^14*b^2 - 90*a^12*b^4 + 150*a^10*b^6 + 136*a^8*b^8 - 118*a^6*b^10 - 70*a^4*b^12 + 18*a^2*b^14 - b^16)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (25*a^11 - 175*a^9*b^2 + 410*a^7*b^4 - 350*a^5*b^6 + 61*a^3*b^8 - 3*a*b^10)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 - (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9 - 100*a^7*b^2 + 110*a^5*b^4 - 20*a^3*b^6 + a*b^8)*cos(d*x + c) + (25*a^8*b - 100*a^6*b^3 + 110*a^4*b^5 - 20*a^2*b^7 + b^9)*sin(d*x + c))/cos(d*x + c)) + 8*(4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*cos(d*x + c)^4 + 2*(5*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2 + ((11*a^4*b - 10*a^2*b^3 + 3*b^5)*cos(d*x + c)^3 + 3*(a^2*b^3 - b^5)*cos(d*x + c))*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8 - 4*a^6*b^2 - 10*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + 2*(3*a^6*b^2 + 5*a^4*b^4 + a^2*b^6 - b^8)*d*cos(d*x + c)^2 + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*d*cos(d*x + c)^3 + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sin(d*x + c))","B",0
551,1,9767,0,3.431211," ","integrate(1/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left({\left(a^{18} + a^{16} b^{2} - 20 \, a^{14} b^{4} - 84 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 154 \, a^{8} b^{10} - 84 \, a^{6} b^{12} - 20 \, a^{4} b^{14} + a^{2} b^{16} + b^{18}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 56 \, a^{12} b^{6} + 84 \, a^{10} b^{8} + 70 \, a^{8} b^{10} + 28 \, a^{6} b^{12} - 4 \, a^{2} b^{16} - b^{18}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{4} + 7 \, a^{12} b^{6} + 21 \, a^{10} b^{8} + 35 \, a^{8} b^{10} + 35 \, a^{6} b^{12} + 21 \, a^{4} b^{14} + 7 \, a^{2} b^{16} + b^{18}\right)} d^{5} + 4 \, {\left({\left(a^{17} b + 6 \, a^{15} b^{3} + 14 \, a^{13} b^{5} + 14 \, a^{11} b^{7} - 14 \, a^{7} b^{11} - 14 \, a^{5} b^{13} - 6 \, a^{3} b^{15} - a b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{3} + 7 \, a^{13} b^{5} + 21 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 35 \, a^{7} b^{11} + 21 \, a^{5} b^{13} + 7 \, a^{3} b^{15} + a b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{22} + 29 \, a^{20} b^{2} + 125 \, a^{18} b^{4} + 315 \, a^{16} b^{6} + 510 \, a^{14} b^{8} + 546 \, a^{12} b^{10} + 378 \, a^{10} b^{12} + 150 \, a^{8} b^{14} + 15 \, a^{6} b^{16} - 15 \, a^{4} b^{18} - 7 \, a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(a^{17} + 8 \, a^{15} b^{2} + 28 \, a^{13} b^{4} + 56 \, a^{11} b^{6} + 70 \, a^{9} b^{8} + 56 \, a^{7} b^{10} + 28 \, a^{5} b^{12} + 8 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(15 \, a^{26} b + 115 \, a^{24} b^{3} + 338 \, a^{22} b^{5} + 354 \, a^{20} b^{7} - 475 \, a^{18} b^{9} - 2055 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} - 2484 \, a^{12} b^{15} - 1047 \, a^{10} b^{17} - 75 \, a^{8} b^{19} + 130 \, a^{6} b^{21} + 50 \, a^{4} b^{23} + 3 \, a^{2} b^{25} - b^{27}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(5 \, a^{21} b + 30 \, a^{19} b^{3} + 61 \, a^{17} b^{5} + 8 \, a^{15} b^{7} - 182 \, a^{13} b^{9} - 364 \, a^{11} b^{11} - 350 \, a^{9} b^{13} - 184 \, a^{7} b^{15} - 47 \, a^{5} b^{17} - 2 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 12 \, \sqrt{2} {\left({\left(a^{18} + a^{16} b^{2} - 20 \, a^{14} b^{4} - 84 \, a^{12} b^{6} - 154 \, a^{10} b^{8} - 154 \, a^{8} b^{10} - 84 \, a^{6} b^{12} - 20 \, a^{4} b^{14} + a^{2} b^{16} + b^{18}\right)} d^{5} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 56 \, a^{12} b^{6} + 84 \, a^{10} b^{8} + 70 \, a^{8} b^{10} + 28 \, a^{6} b^{12} - 4 \, a^{2} b^{16} - b^{18}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{14} b^{4} + 7 \, a^{12} b^{6} + 21 \, a^{10} b^{8} + 35 \, a^{8} b^{10} + 35 \, a^{6} b^{12} + 21 \, a^{4} b^{14} + 7 \, a^{2} b^{16} + b^{18}\right)} d^{5} + 4 \, {\left({\left(a^{17} b + 6 \, a^{15} b^{3} + 14 \, a^{13} b^{5} + 14 \, a^{11} b^{7} - 14 \, a^{7} b^{11} - 14 \, a^{5} b^{13} - 6 \, a^{3} b^{15} - a b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + {\left(a^{15} b^{3} + 7 \, a^{13} b^{5} + 21 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 35 \, a^{7} b^{11} + 21 \, a^{5} b^{13} + 7 \, a^{3} b^{15} + a b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(5 \, a^{20} + 30 \, a^{18} b^{2} + 61 \, a^{16} b^{4} + 8 \, a^{14} b^{6} - 182 \, a^{12} b^{8} - 364 \, a^{10} b^{10} - 350 \, a^{8} b^{12} - 184 \, a^{6} b^{14} - 47 \, a^{4} b^{16} - 2 \, a^{2} b^{18} + b^{20}\right)} d^{4} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + {\left(5 \, a^{15} + 15 \, a^{13} b^{2} + a^{11} b^{4} - 45 \, a^{9} b^{6} - 65 \, a^{7} b^{8} - 35 \, a^{5} b^{10} - 5 \, a^{3} b^{12} + a b^{14}\right)} d^{2} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{22} + 29 \, a^{20} b^{2} + 125 \, a^{18} b^{4} + 315 \, a^{16} b^{6} + 510 \, a^{14} b^{8} + 546 \, a^{12} b^{10} + 378 \, a^{10} b^{12} + 150 \, a^{8} b^{14} + 15 \, a^{6} b^{16} - 15 \, a^{4} b^{18} - 7 \, a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(a^{17} + 8 \, a^{15} b^{2} + 28 \, a^{13} b^{4} + 56 \, a^{11} b^{6} + 70 \, a^{9} b^{8} + 56 \, a^{7} b^{10} + 28 \, a^{5} b^{12} + 8 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(15 \, a^{26} b + 115 \, a^{24} b^{3} + 338 \, a^{22} b^{5} + 354 \, a^{20} b^{7} - 475 \, a^{18} b^{9} - 2055 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} - 2484 \, a^{12} b^{15} - 1047 \, a^{10} b^{17} - 75 \, a^{8} b^{19} + 130 \, a^{6} b^{21} + 50 \, a^{4} b^{23} + 3 \, a^{2} b^{25} - b^{27}\right)} d^{7} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} + 2 \, {\left(5 \, a^{21} b + 30 \, a^{19} b^{3} + 61 \, a^{17} b^{5} + 8 \, a^{15} b^{7} - 182 \, a^{13} b^{9} - 364 \, a^{11} b^{11} - 350 \, a^{9} b^{13} - 184 \, a^{7} b^{15} - 47 \, a^{5} b^{17} - 2 \, a^{3} b^{19} + a b^{21}\right)} d^{5} \sqrt{\frac{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}{{\left(a^{20} + 10 \, a^{18} b^{2} + 45 \, a^{16} b^{4} + 120 \, a^{14} b^{6} + 210 \, a^{12} b^{8} + 252 \, a^{10} b^{10} + 210 \, a^{8} b^{12} + 120 \, a^{6} b^{14} + 45 \, a^{4} b^{16} + 10 \, a^{2} b^{18} + b^{20}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{3}{4}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} - 4 \, a^{6} b^{2} - 10 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{13} - 14 \, a^{11} b^{2} + 35 \, a^{9} b^{4} + 76 \, a^{7} b^{6} - 9 \, a^{5} b^{8} - 30 \, a^{3} b^{10} + 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{2} - 25 \, a^{9} b^{4} - 34 \, a^{7} b^{6} + 14 \, a^{5} b^{8} + 15 \, a^{3} b^{10} - 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{4} - 8 \, a^{7} b^{6} - 14 \, a^{5} b^{8} + 5 \, a b^{12}\right)} d^{3} + 4 \, {\left({\left(a^{12} b - 9 \, a^{10} b^{3} - 6 \, a^{8} b^{5} + 14 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{3} - 8 \, a^{8} b^{5} - 14 \, a^{6} b^{7} + 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} - 4 \, a^{6} b^{2} - 10 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - {\left({\left(a^{13} - 14 \, a^{11} b^{2} + 35 \, a^{9} b^{4} + 76 \, a^{7} b^{6} - 9 \, a^{5} b^{8} - 30 \, a^{3} b^{10} + 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{11} b^{2} - 25 \, a^{9} b^{4} - 34 \, a^{7} b^{6} + 14 \, a^{5} b^{8} + 15 \, a^{3} b^{10} - 5 \, a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{9} b^{4} - 8 \, a^{7} b^{6} - 14 \, a^{5} b^{8} + 5 \, a b^{12}\right)} d^{3} + 4 \, {\left({\left(a^{12} b - 9 \, a^{10} b^{3} - 6 \, a^{8} b^{5} + 14 \, a^{6} b^{7} + 5 \, a^{4} b^{9} - 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{3} + {\left(a^{10} b^{3} - 8 \, a^{8} b^{5} - 14 \, a^{6} b^{7} + 5 \, a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(25 \, a^{14} b^{2} - 25 \, a^{12} b^{4} - 115 \, a^{10} b^{6} + 35 \, a^{8} b^{8} + 171 \, a^{6} b^{10} + 53 \, a^{4} b^{12} - 17 \, a^{2} b^{14} + b^{16}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(25 \, a^{15} b^{3} - 25 \, a^{13} b^{5} - 115 \, a^{11} b^{7} + 35 \, a^{9} b^{9} + 171 \, a^{7} b^{11} + 53 \, a^{5} b^{13} - 17 \, a^{3} b^{15} + a b^{17}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(75 \, a^{10} b^{3} - 325 \, a^{8} b^{5} + 430 \, a^{6} b^{7} - 170 \, a^{4} b^{9} + 23 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10} + {\left(a^{15} - 5 \, a^{13} b^{2} - 35 \, a^{11} b^{4} - 65 \, a^{9} b^{6} - 45 \, a^{7} b^{8} + a^{5} b^{10} + 15 \, a^{3} b^{12} + 5 \, a b^{14}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}}}{25 \, a^{8} b^{2} - 100 \, a^{6} b^{4} + 110 \, a^{4} b^{6} - 20 \, a^{2} b^{8} + b^{10}}} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(25 \, a^{9} b^{2} - 100 \, a^{7} b^{4} + 110 \, a^{5} b^{6} - 20 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left(25 \, a^{8} b^{3} - 100 \, a^{6} b^{5} + 110 \, a^{4} b^{7} - 20 \, a^{2} b^{9} + b^{11}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left({\left(7 \, a^{4} b - 18 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(19 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{4} \cos\left(d x + c\right) + 2 \, {\left(5 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} - 4 \, a^{6} b^{2} - 10 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(12*sqrt(2)*((a^18 + a^16*b^2 - 20*a^14*b^4 - 84*a^12*b^6 - 154*a^10*b^8 - 154*a^8*b^10 - 84*a^6*b^12 - 20*a^4*b^14 + a^2*b^16 + b^18)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^2 + 20*a^14*b^4 + 56*a^12*b^6 + 84*a^10*b^8 + 70*a^8*b^10 + 28*a^6*b^12 - 4*a^2*b^16 - b^18)*d^5*cos(d*x + c)^2 + (a^14*b^4 + 7*a^12*b^6 + 21*a^10*b^8 + 35*a^8*b^10 + 35*a^6*b^12 + 21*a^4*b^14 + 7*a^2*b^16 + b^18)*d^5 + 4*((a^17*b + 6*a^15*b^3 + 14*a^13*b^5 + 14*a^11*b^7 - 14*a^7*b^11 - 14*a^5*b^13 - 6*a^3*b^15 - a*b^17)*d^5*cos(d*x + c)^3 + (a^15*b^3 + 7*a^13*b^5 + 21*a^11*b^7 + 35*a^9*b^9 + 35*a^7*b^11 + 21*a^5*b^13 + 7*a^3*b^15 + a*b^17)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) - sqrt(2)*((3*a^22 + 29*a^20*b^2 + 125*a^18*b^4 + 315*a^16*b^6 + 510*a^14*b^8 + 546*a^12*b^10 + 378*a^10*b^12 + 150*a^8*b^14 + 15*a^6*b^16 - 15*a^4*b^18 - 7*a^2*b^20 - b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(a^17 + 8*a^15*b^2 + 28*a^13*b^4 + 56*a^11*b^6 + 70*a^9*b^8 + 56*a^7*b^10 + 28*a^5*b^12 + 8*a^3*b^14 + a*b^16)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) + sqrt(2)*((15*a^26*b + 115*a^24*b^3 + 338*a^22*b^5 + 354*a^20*b^7 - 475*a^18*b^9 - 2055*a^16*b^11 - 3060*a^14*b^13 - 2484*a^12*b^15 - 1047*a^10*b^17 - 75*a^8*b^19 + 130*a^6*b^21 + 50*a^4*b^23 + 3*a^2*b^25 - b^27)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(5*a^21*b + 30*a^19*b^3 + 61*a^17*b^5 + 8*a^15*b^7 - 182*a^13*b^9 - 364*a^11*b^11 - 350*a^9*b^13 - 184*a^7*b^15 - 47*a^5*b^17 - 2*a^3*b^19 + a*b^21)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 12*sqrt(2)*((a^18 + a^16*b^2 - 20*a^14*b^4 - 84*a^12*b^6 - 154*a^10*b^8 - 154*a^8*b^10 - 84*a^6*b^12 - 20*a^4*b^14 + a^2*b^16 + b^18)*d^5*cos(d*x + c)^4 + 2*(3*a^16*b^2 + 20*a^14*b^4 + 56*a^12*b^6 + 84*a^10*b^8 + 70*a^8*b^10 + 28*a^6*b^12 - 4*a^2*b^16 - b^18)*d^5*cos(d*x + c)^2 + (a^14*b^4 + 7*a^12*b^6 + 21*a^10*b^8 + 35*a^8*b^10 + 35*a^6*b^12 + 21*a^4*b^14 + 7*a^2*b^16 + b^18)*d^5 + 4*((a^17*b + 6*a^15*b^3 + 14*a^13*b^5 + 14*a^11*b^7 - 14*a^7*b^11 - 14*a^5*b^13 - 6*a^3*b^15 - a*b^17)*d^5*cos(d*x + c)^3 + (a^15*b^3 + 7*a^13*b^5 + 21*a^11*b^7 + 35*a^9*b^9 + 35*a^7*b^11 + 21*a^5*b^13 + 7*a^3*b^15 + a*b^17)*d^5*cos(d*x + c))*sin(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4)*arctan(-((5*a^20 + 30*a^18*b^2 + 61*a^16*b^4 + 8*a^14*b^6 - 182*a^12*b^8 - 364*a^10*b^10 - 350*a^8*b^12 - 184*a^6*b^14 - 47*a^4*b^16 - 2*a^2*b^18 + b^20)*d^4*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + (5*a^15 + 15*a^13*b^2 + a^11*b^4 - 45*a^9*b^6 - 65*a^7*b^8 - 35*a^5*b^10 - 5*a^3*b^12 + a*b^14)*d^2*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)) + sqrt(2)*((3*a^22 + 29*a^20*b^2 + 125*a^18*b^4 + 315*a^16*b^6 + 510*a^14*b^8 + 546*a^12*b^10 + 378*a^10*b^12 + 150*a^8*b^14 + 15*a^6*b^16 - 15*a^4*b^18 - 7*a^2*b^20 - b^22)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(a^17 + 8*a^15*b^2 + 28*a^13*b^4 + 56*a^11*b^6 + 70*a^9*b^8 + 56*a^7*b^10 + 28*a^5*b^12 + 8*a^3*b^14 + a*b^16)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4) - sqrt(2)*((15*a^26*b + 115*a^24*b^3 + 338*a^22*b^5 + 354*a^20*b^7 - 475*a^18*b^9 - 2055*a^16*b^11 - 3060*a^14*b^13 - 2484*a^12*b^15 - 1047*a^10*b^17 - 75*a^8*b^19 + 130*a^6*b^21 + 50*a^4*b^23 + 3*a^2*b^25 - b^27)*d^7*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)) + 2*(5*a^21*b + 30*a^19*b^3 + 61*a^17*b^5 + 8*a^15*b^7 - 182*a^13*b^9 - 364*a^11*b^11 - 350*a^9*b^13 - 184*a^7*b^15 - 47*a^5*b^17 - 2*a^3*b^19 + a*b^21)*d^5*sqrt((25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)/((a^20 + 10*a^18*b^2 + 45*a^16*b^4 + 120*a^14*b^6 + 210*a^12*b^8 + 252*a^10*b^10 + 210*a^8*b^12 + 120*a^6*b^14 + 45*a^4*b^16 + 10*a^2*b^18 + b^20)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(3/4))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10)) + 3*sqrt(2)*((a^8 - 4*a^6*b^2 - 10*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + 2*(3*a^6*b^2 + 5*a^4*b^4 + a^2*b^6 - b^8)*d*cos(d*x + c)^2 + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*d*cos(d*x + c)^3 + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sin(d*x + c) - ((a^13 - 14*a^11*b^2 + 35*a^9*b^4 + 76*a^7*b^6 - 9*a^5*b^8 - 30*a^3*b^10 + 5*a*b^12)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^2 - 25*a^9*b^4 - 34*a^7*b^6 + 14*a^5*b^8 + 15*a^3*b^10 - 5*a*b^12)*d^3*cos(d*x + c)^2 + (a^9*b^4 - 8*a^7*b^6 - 14*a^5*b^8 + 5*a*b^12)*d^3 + 4*((a^12*b - 9*a^10*b^3 - 6*a^8*b^5 + 14*a^6*b^7 + 5*a^4*b^9 - 5*a^2*b^11)*d^3*cos(d*x + c)^3 + (a^10*b^3 - 8*a^8*b^5 - 14*a^6*b^7 + 5*a^2*b^11)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^8 - 4*a^6*b^2 - 10*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + 2*(3*a^6*b^2 + 5*a^4*b^4 + a^2*b^6 - b^8)*d*cos(d*x + c)^2 + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*d*cos(d*x + c)^3 + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sin(d*x + c) - ((a^13 - 14*a^11*b^2 + 35*a^9*b^4 + 76*a^7*b^6 - 9*a^5*b^8 - 30*a^3*b^10 + 5*a*b^12)*d^3*cos(d*x + c)^4 + 2*(3*a^11*b^2 - 25*a^9*b^4 - 34*a^7*b^6 + 14*a^5*b^8 + 15*a^3*b^10 - 5*a*b^12)*d^3*cos(d*x + c)^2 + (a^9*b^4 - 8*a^7*b^6 - 14*a^5*b^8 + 5*a*b^12)*d^3 + 4*((a^12*b - 9*a^10*b^3 - 6*a^8*b^5 + 14*a^6*b^7 + 5*a^4*b^9 - 5*a^2*b^11)*d^3*cos(d*x + c)^3 + (a^10*b^3 - 8*a^8*b^5 - 14*a^6*b^7 + 5*a^2*b^11)*d^3*cos(d*x + c))*sin(d*x + c))*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4)*log(((25*a^14*b^2 - 25*a^12*b^4 - 115*a^10*b^6 + 35*a^8*b^8 + 171*a^6*b^10 + 53*a^4*b^12 - 17*a^2*b^14 + b^16)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) - sqrt(2)*(2*(25*a^15*b^3 - 25*a^13*b^5 - 115*a^11*b^7 + 35*a^9*b^9 + 171*a^7*b^11 + 53*a^5*b^13 - 17*a^3*b^15 + a*b^17)*d^3*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))*cos(d*x + c) + (75*a^10*b^3 - 325*a^8*b^5 + 430*a^6*b^7 - 170*a^4*b^9 + 23*a^2*b^11 - b^13)*d*cos(d*x + c))*sqrt((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10 + (a^15 - 5*a^13*b^2 - 35*a^11*b^4 - 65*a^9*b^6 - 45*a^7*b^8 + a^5*b^10 + 15*a^3*b^12 + 5*a*b^14)*d^2*sqrt(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4)))/(25*a^8*b^2 - 100*a^6*b^4 + 110*a^4*b^6 - 20*a^2*b^8 + b^10))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/((a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10)*d^4))^(1/4) + (25*a^9*b^2 - 100*a^7*b^4 + 110*a^5*b^6 - 20*a^3*b^8 + a*b^10)*cos(d*x + c) + (25*a^8*b^3 - 100*a^6*b^5 + 110*a^4*b^7 - 20*a^2*b^9 + b^11)*sin(d*x + c))/cos(d*x + c)) - 8*((7*a^4*b - 18*a^2*b^3 - b^5)*cos(d*x + c)^4 + (19*a^2*b^3 + b^5)*cos(d*x + c)^2 + 2*(3*a*b^4*cos(d*x + c) + 2*(5*a^3*b^2 - a*b^4)*cos(d*x + c)^3)*sin(d*x + c))*sqrt((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/((a^8 - 4*a^6*b^2 - 10*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + 2*(3*a^6*b^2 + 5*a^4*b^4 + a^2*b^6 - b^8)*d*cos(d*x + c)^2 + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*d*cos(d*x + c)^3 + (a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c))*sin(d*x + c))","B",0
552,-1,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,1,2847,0,0.567636," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} d^{5} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} d^{5} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) \cos\left(d x + c\right)^{2} - 15 \, \sqrt{2} {\left(2 \, a b d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 15 \, \sqrt{2} {\left(2 \, a b d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{4} b + 6 \, a^{2} b^{3} + 3 \, b^{5} - 18 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*d^5*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12))*cos(d*x + c)^2 + 60*sqrt(2)*d^5*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12))*cos(d*x + c)^2 - 15*sqrt(2)*(2*a*b*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + 15*sqrt(2)*(2*a*b*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(3*a^4*b + 6*a^2*b^3 + 3*b^5 - 18*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2 + 5*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)","B",0
556,1,2757,0,0.605124," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} d^{5} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d^{5} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left(2 \, a b d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left(2 \, a b d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*d^5*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12))*cos(d*x + c) + 12*sqrt(2)*d^5*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12))*cos(d*x + c) + 3*sqrt(2)*(2*a*b*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(2*a*b*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - 8*(3*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c))","B",0
557,1,2729,0,0.591793," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) - \sqrt{2} {\left(2 \, a b d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, a b d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/4*(4*sqrt(2)*d^5*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*d^5*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) - sqrt(2)*(2*a*b*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + (a^4 + 2*a^2*b^2 + b^4)*d)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*a*b*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + (a^4 + 2*a^2*b^2 + b^4)*d)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + 8*(a^4*b + 2*a^2*b^3 + b^5)*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + 2*a^2*b^2 + b^4)*d)","B",0
558,1,2640,0,0.568820," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{4} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} d^{4} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + \sqrt{2} {\left(2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/4*(4*sqrt(2)*d^4*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*d^4*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + sqrt(2)*(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
559,1,2883,0,0.541904," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) - 8 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 2 \, {\left(a b d^{3} \cos\left(d x + c\right)^{2} - a b d^{3}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 2 \, {\left(a b d^{3} \cos\left(d x + c\right)^{2} - a b d^{3}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)}}"," ",0,"-1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) - 8*(a^5 + 2*a^3*b^2 + a*b^4)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 + 2*a^2*b^2 + b^4)*d + 2*(a*b*d^3*cos(d*x + c)^2 - a*b*d^3)*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 + 2*a^2*b^2 + b^4)*d + 2*(a*b*d^3*cos(d*x + c)^2 - a*b*d^3)*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)))/((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 + 2*a^2*b^2 + b^4)*d)","B",0
560,1,2861,0,0.550030," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) - 3 \, \sqrt{2} {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d - 2 \, {\left(a b d^{3} \cos\left(d x + c\right)^{2} - a b d^{3}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d - 2 \, {\left(a b d^{3} \cos\left(d x + c\right)^{2} - a b d^{3}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)}}"," ",0,"-1/12*(12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) - 3*sqrt(2)*((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 + 2*a^2*b^2 + b^4)*d - 2*(a*b*d^3*cos(d*x + c)^2 - a*b*d^3)*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 + 2*a^2*b^2 + b^4)*d - 2*(a*b*d^3*cos(d*x + c)^2 - a*b*d^3)*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - 8*((a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^2 + 3*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 - (a^4 + 2*a^2*b^2 + b^4)*d)","B",0
561,1,3096,0,0.691787," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{60 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 60 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(b d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{3} + a b^{2}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{4} b - b^{5}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) - 15 \, \sqrt{2} {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 2 \, {\left(a b d^{3} \cos\left(d x + c\right)^{4} - 2 \, a b d^{3} \cos\left(d x + c\right)^{2} + a b d^{3}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 15 \, \sqrt{2} {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 2 \, {\left(a b d^{3} \cos\left(d x + c\right)^{4} - 2 \, a b d^{3} \cos\left(d x + c\right)^{2} + a b d^{3}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(5 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(6 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)}}"," ",0,"1/60*(60*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 60*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(b*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^3 + a*b^2)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^4*b - b^5)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) - 15*sqrt(2)*((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^4 - 2*(a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d + 2*(a*b*d^3*cos(d*x + c)^4 - 2*a*b*d^3*cos(d*x + c)^2 + a*b*d^3)*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + 15*sqrt(2)*((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^4 - 2*(a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d + 2*(a*b*d^3*cos(d*x + c)^4 - 2*a*b*d^3*cos(d*x + c)^2 + a*b*d^3)*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^5 - 2*a^3*b^2 + a*b^4)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) + 8*(5*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 - 5*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2 - 3*(6*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^3 - 5*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^4 - 2*(a^4 + 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)","B",0
562,1,5080,0,1.189690," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{420 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) \cos\left(d x + c\right)^{3} + 105 \, \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right)^{3} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 105 \, \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right)^{3} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(252 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{3} - 42 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) - 5 \, {\left(3 \, a^{8} b^{2} + 12 \, a^{6} b^{4} + 18 \, a^{4} b^{6} + 12 \, a^{2} b^{8} + 3 \, b^{10} + {\left(7 \, a^{10} + 18 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 32 \, a^{4} b^{6} - 33 \, a^{2} b^{8} - 10 \, b^{10}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{420 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"1/420*(420*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24))*cos(d*x + c)^3 + 420*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24))*cos(d*x + c)^3 + 105*sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c)^3 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 105*sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c)^3 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 8*(252*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c)^3 - 42*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c) - 5*(3*a^8*b^2 + 12*a^6*b^4 + 18*a^4*b^6 + 12*a^2*b^8 + 3*b^10 + (7*a^10 + 18*a^8*b^2 + 2*a^6*b^4 - 32*a^4*b^6 - 33*a^2*b^8 - 10*b^10)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^3)","B",0
563,1,5043,0,0.637935," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) \cos\left(d x + c\right)^{2} + 15 \, \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{8} b^{2} + 12 \, a^{6} b^{4} + 18 \, a^{4} b^{6} + 12 \, a^{2} b^{8} + 3 \, b^{10} + 3 \, {\left(5 \, a^{10} + 14 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 16 \, a^{4} b^{6} - 19 \, a^{2} b^{8} - 6 \, b^{10}\right)} \cos\left(d x + c\right)^{2} + 10 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/60*(60*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*((a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24))*cos(d*x + c)^2 + 60*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*((a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24))*cos(d*x + c)^2 + 15*sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 8*(3*a^8*b^2 + 12*a^6*b^4 + 18*a^4*b^6 + 12*a^2*b^8 + 3*b^10 + 3*(5*a^10 + 14*a^8*b^2 + 6*a^6*b^4 - 16*a^4*b^6 - 19*a^2*b^8 - 6*b^10)*cos(d*x + c)^2 + 10*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2)","B",0
564,1,4967,0,1.067926," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(6 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24))*cos(d*x + c) + 12*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24))*cos(d*x + c) + 3*sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 8*(6*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c))","B",0
565,1,4881,0,0.638271," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + 4 \, \sqrt{2} d^{5} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(4 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d}"," ",0,"1/4*(4*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*((a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + 4*sqrt(2)*d^5*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*((a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4) - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(4*(a^3*b - a*b^3)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4) - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) + 8*(a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)","B",0
566,1,5093,0,1.105130," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + 8 \, {\left(a^{10} + 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d\right)}}"," ",0,"1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + 8*(a^10 + 4*a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 + a^2*b^8)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d + 4*((a^3*b - a*b^3)*d^3*cos(d*x + c)^2 - (a^3*b - a*b^3)*d^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d + 4*((a^3*b - a*b^3)*d^3*cos(d*x + c)^2 - (a^3*b - a*b^3)*d^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)","B",0
567,1,5149,0,0.664164," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + 12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) - 3 \, \sqrt{2} {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d - 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left({\left(a^{10} + 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d\right)}}"," ",0,"-1/12*(12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*((a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + 12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*((a^2 - b^2)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*((a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) - 3*sqrt(2)*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 4*((a^3*b - a*b^3)*d^3*cos(d*x + c)^2 - (a^3*b - a*b^3)*d^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d - 4*((a^3*b - a*b^3)*d^3*cos(d*x + c)^2 - (a^3*b - a*b^3)*d^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*(2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 8*((a^10 + 4*a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 + a^2*b^8)*cos(d*x + c)^2 + 6*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)","B",0
568,1,5441,0,1.115306," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} - \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + 60 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + \sqrt{2} {\left(2 \, a b d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} - 10 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d^{7} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}} + {\left(a^{14} - 3 \, a^{12} b^{2} - 15 \, a^{10} b^{4} - 11 \, a^{8} b^{6} + 11 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 3 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{3}{4}}}{a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}}\right) + 15 \, \sqrt{2} {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}} \cos\left(d x + c\right) + 2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(10 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{4} - 10 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(6 \, a^{10} + 19 \, a^{8} b^{2} + 16 \, a^{6} b^{4} - 6 \, a^{4} b^{6} - 14 \, a^{2} b^{8} - 5 \, b^{10}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left({\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d\right)}}"," ",0,"-1/60*(60*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) - sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) + sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + 60*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + sqrt(2)*(2*a*b*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^6 + a^4*b^2 - a^2*b^4 - b^6)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4) - sqrt(2)*(2*(a^9*b - 4*a^7*b^3 - 10*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d^7*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4) + (a^14 - 3*a^12*b^2 - 15*a^10*b^4 - 11*a^8*b^6 + 11*a^6*b^8 + 15*a^4*b^10 + 3*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(3/4))/(a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)) + 15*sqrt(2)*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 - 2*(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d + 4*((a^3*b - a*b^3)*d^3*cos(d*x + c)^4 - 2*(a^3*b - a*b^3)*d^3*cos(d*x + c)^2 + (a^3*b - a*b^3)*d^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 - 2*(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d + 4*((a^3*b - a*b^3)*d^3*cos(d*x + c)^4 - 2*(a^3*b - a*b^3)*d^3*cos(d*x + c)^2 + (a^3*b - a*b^3)*d^3)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) - sqrt(2)*((a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)*cos(d*x + c) + 2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^3*b - a*b^3)*d^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/d^4)^(1/4) + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*sin(d*x + c))/cos(d*x + c)) - 8*(10*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c)^4 - 10*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*cos(d*x + c)^2 - 3*((6*a^10 + 19*a^8*b^2 + 16*a^6*b^4 - 6*a^4*b^6 - 14*a^2*b^8 - 5*b^10)*cos(d*x + c)^3 - 5*(a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^4 - 2*(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*cos(d*x + c)^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)","B",0
569,1,7332,0,2.751456," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{1260 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{4} + 1260 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{4} + 315 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right)^{4} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 315 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right)^{4} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(35 \, a^{12} b^{3} + 210 \, a^{10} b^{5} + 525 \, a^{8} b^{7} + 700 \, a^{6} b^{9} + 525 \, a^{4} b^{11} + 210 \, a^{2} b^{13} + 35 \, b^{15} - 7 \, {\left(162 \, a^{14} b + 913 \, a^{12} b^{3} + 2076 \, a^{10} b^{5} + 2355 \, a^{8} b^{7} + 1250 \, a^{6} b^{9} + 87 \, a^{4} b^{11} - 192 \, a^{2} b^{13} - 59 \, b^{15}\right)} \cos\left(d x + c\right)^{4} + 7 \, {\left(27 \, a^{14} b + 143 \, a^{12} b^{3} + 291 \, a^{10} b^{5} + 255 \, a^{8} b^{7} + 25 \, a^{6} b^{9} - 123 \, a^{4} b^{11} - 87 \, a^{2} b^{13} - 19 \, b^{15}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(7 \, a^{15} + 12 \, a^{13} b^{2} - 75 \, a^{11} b^{4} - 310 \, a^{9} b^{6} - 495 \, a^{7} b^{8} - 408 \, a^{5} b^{10} - 173 \, a^{3} b^{12} - 30 \, a b^{14}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{1260 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/1260*(1260*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c)^4 + 1260*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c)^4 + 315*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c)^4 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 315*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c)^4 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) + 8*(35*a^12*b^3 + 210*a^10*b^5 + 525*a^8*b^7 + 700*a^6*b^9 + 525*a^4*b^11 + 210*a^2*b^13 + 35*b^15 - 7*(162*a^14*b + 913*a^12*b^3 + 2076*a^10*b^5 + 2355*a^8*b^7 + 1250*a^6*b^9 + 87*a^4*b^11 - 192*a^2*b^13 - 59*b^15)*cos(d*x + c)^4 + 7*(27*a^14*b + 143*a^12*b^3 + 291*a^10*b^5 + 255*a^8*b^7 + 25*a^6*b^9 - 123*a^4*b^11 - 87*a^2*b^13 - 19*b^15)*cos(d*x + c)^2 + 15*((7*a^15 + 12*a^13*b^2 - 75*a^11*b^4 - 310*a^9*b^6 - 495*a^7*b^8 - 408*a^5*b^10 - 173*a^3*b^12 - 30*a*b^14)*cos(d*x + c)^3 + 9*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4)","B",0
570,1,7272,0,2.825356," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{420 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{3} + 420 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{3} - 105 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 105 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right)^{3} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(21 \, {\left(5 \, a^{15} + 12 \, a^{13} b^{2} - 33 \, a^{11} b^{4} - 170 \, a^{9} b^{6} - 285 \, a^{7} b^{8} - 240 \, a^{5} b^{10} - 103 \, a^{3} b^{12} - 18 \, a b^{14}\right)} \cos\left(d x + c\right)^{3} + 63 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) + 5 \, {\left(3 \, a^{12} b^{3} + 18 \, a^{10} b^{5} + 45 \, a^{8} b^{7} + 60 \, a^{6} b^{9} + 45 \, a^{4} b^{11} + 18 \, a^{2} b^{13} + 3 \, b^{15} + {\left(21 \, a^{14} b + 116 \, a^{12} b^{3} + 255 \, a^{10} b^{5} + 270 \, a^{8} b^{7} + 115 \, a^{6} b^{9} - 24 \, a^{4} b^{11} - 39 \, a^{2} b^{13} - 10 \, b^{15}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{420 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{3}}"," ",0,"1/420*(420*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c)^3 + 420*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c)^3 - 105*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c)^3 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) + 105*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c)^3 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) + 8*(21*(5*a^15 + 12*a^13*b^2 - 33*a^11*b^4 - 170*a^9*b^6 - 285*a^7*b^8 - 240*a^5*b^10 - 103*a^3*b^12 - 18*a*b^14)*cos(d*x + c)^3 + 63*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*cos(d*x + c) + 5*(3*a^12*b^3 + 18*a^10*b^5 + 45*a^8*b^7 + 60*a^6*b^9 + 45*a^4*b^11 + 18*a^2*b^13 + 3*b^15 + (21*a^14*b + 116*a^12*b^3 + 255*a^10*b^5 + 270*a^8*b^7 + 115*a^6*b^9 - 24*a^4*b^11 - 39*a^2*b^13 - 10*b^15)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^3)","B",0
571,1,7179,0,2.763110," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{2} + 20 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right)^{2} + 5 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 5 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15} + 3 \, {\left(5 \, a^{14} b + 28 \, a^{12} b^{3} + 63 \, a^{10} b^{5} + 70 \, a^{8} b^{7} + 35 \, a^{6} b^{9} - 7 \, a^{2} b^{13} - 2 \, b^{15}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{20 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/20*(20*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c)^2 + 20*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c)^2 + 5*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 5*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 8*(a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15 + 3*(5*a^14*b + 28*a^12*b^3 + 63*a^10*b^5 + 70*a^8*b^7 + 35*a^6*b^9 - 7*a^2*b^13 - 2*b^15)*cos(d*x + c)^2 + 5*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2)","B",0
572,1,7117,0,2.701644," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} d^{5} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) \cos\left(d x + c\right) - 3 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left(2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(9 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right) + {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)}"," ",0,"-1/12*(12*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c) + 12*sqrt(2)*d^5*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36))*cos(d*x + c) - 3*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*(2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 8*(9*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*cos(d*x + c) + (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c))","B",0
573,1,7395,0,2.650896," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 4 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d + 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d + 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15} - {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{15} + 6 \, a^{13} b^{2} + 15 \, a^{11} b^{4} + 20 \, a^{9} b^{6} + 15 \, a^{7} b^{8} + 6 \, a^{5} b^{10} + a^{3} b^{12}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"1/4*(4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 4*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d + 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 - (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d + 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 - (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 8*(a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15 - (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*cos(d*x + c)^2 - (a^15 + 6*a^13*b^2 + 15*a^11*b^4 + 20*a^9*b^6 + 15*a^7*b^8 + 6*a^5*b^10 + a^3*b^12)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d)","B",0
574,1,7355,0,2.688337," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 12 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 3 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left({\left(a^{15} + 6 \, a^{13} b^{2} + 15 \, a^{11} b^{4} + 20 \, a^{9} b^{6} + 15 \, a^{7} b^{8} + 6 \, a^{5} b^{10} + a^{3} b^{12}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"1/12*(12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 12*sqrt(2)*(d^5*cos(d*x + c)^2 - d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 3*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 - (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 - (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) + 8*((a^15 + 6*a^13*b^2 + 15*a^11*b^4 + 20*a^9*b^6 + 15*a^7*b^8 + 6*a^5*b^10 + a^3*b^12)*cos(d*x + c)^2 + 9*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d)","B",0
575,1,7742,0,2.722634," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 20 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 5 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d + 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 5 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d + 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(5 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, {\left(2 \, a^{15} + 7 \, a^{13} b^{2} - 35 \, a^{9} b^{6} - 70 \, a^{7} b^{8} - 63 \, a^{5} b^{10} - 28 \, a^{3} b^{12} - 5 \, a b^{14}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(a^{15} + 3 \, a^{13} b^{2} - 3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 45 \, a^{7} b^{8} - 39 \, a^{5} b^{10} - 17 \, a^{3} b^{12} - 3 \, a b^{14}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{20 \, {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"-1/20*(20*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 20*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 5*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 2*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d + 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^4 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 + (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 5*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 2*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d + 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^4 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 + (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 8*(5*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*cos(d*x + c)^4 - 5*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*cos(d*x + c)^2 - (3*(2*a^15 + 7*a^13*b^2 - 35*a^9*b^6 - 70*a^7*b^8 - 63*a^5*b^10 - 28*a^3*b^12 - 5*a*b^14)*cos(d*x + c)^3 - 5*(a^15 + 3*a^13*b^2 - 3*a^11*b^4 - 25*a^9*b^6 - 45*a^7*b^8 - 39*a^5*b^10 - 17*a^3*b^12 - 3*a*b^14)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 2*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d)","B",0
576,1,7771,0,2.709274," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{420 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 420 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{4} - 2 \, d^{5} \cos\left(d x + c\right)^{2} + d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(a^{3} - 3 \, a b^{2}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{8} b + 8 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - b^{9}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{15} - 15 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 81 \, a^{9} b^{6} + 27 \, a^{7} b^{8} - 69 \, a^{5} b^{10} - 37 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - {\left(3 \, a^{20} b - 28 \, a^{18} b^{3} - 171 \, a^{16} b^{5} - 288 \, a^{14} b^{7} - 82 \, a^{12} b^{9} + 264 \, a^{10} b^{11} + 282 \, a^{8} b^{13} + 64 \, a^{6} b^{15} - 33 \, a^{4} b^{17} - 12 \, a^{2} b^{19} + b^{21}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 105 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 105 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d - 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(3 \, a^{14} b - 91 \, a^{12} b^{3} + 795 \, a^{10} b^{5} - 1611 \, a^{8} b^{7} + 1217 \, a^{6} b^{9} - 345 \, a^{4} b^{11} + 33 \, a^{2} b^{13} - b^{15}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{21} - 30 \, a^{19} b^{2} + 249 \, a^{17} b^{4} - 280 \, a^{15} b^{6} - 1038 \, a^{13} b^{8} + 732 \, a^{11} b^{10} + 1322 \, a^{9} b^{12} - 504 \, a^{7} b^{14} - 531 \, a^{5} b^{16} + 82 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} + 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(5 \, {\left(10 \, a^{15} + 39 \, a^{13} b^{2} + 24 \, a^{11} b^{4} - 115 \, a^{9} b^{6} - 270 \, a^{7} b^{8} - 255 \, a^{5} b^{10} - 116 \, a^{3} b^{12} - 21 \, a b^{14}\right)} \cos\left(d x + c\right)^{4} - 35 \, {\left(a^{15} + 3 \, a^{13} b^{2} - 3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 45 \, a^{7} b^{8} - 39 \, a^{5} b^{10} - 17 \, a^{3} b^{12} - 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{2} + 21 \, {\left({\left(18 \, a^{14} b + 103 \, a^{12} b^{3} + 240 \, a^{10} b^{5} + 285 \, a^{8} b^{7} + 170 \, a^{6} b^{9} + 33 \, a^{4} b^{11} - 12 \, a^{2} b^{13} - 5 \, b^{15}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(3 \, a^{14} b + 17 \, a^{12} b^{3} + 39 \, a^{10} b^{5} + 45 \, a^{8} b^{7} + 25 \, a^{6} b^{9} + 3 \, a^{4} b^{11} - 3 \, a^{2} b^{13} - b^{15}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{420 \, {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"-1/420*(420*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 420*sqrt(2)*(d^5*cos(d*x + c)^4 - 2*d^5*cos(d*x + c)^2 + d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((a^3 - 3*a*b^2)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^8*b + 8*a^6*b^3 + 6*a^4*b^5 - b^9)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((a^15 - 15*a^13*b^2 + 9*a^11*b^4 + 81*a^9*b^6 + 27*a^7*b^8 - 69*a^5*b^10 - 37*a^3*b^12 + 3*a*b^14)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - (3*a^20*b - 28*a^18*b^3 - 171*a^16*b^5 - 288*a^14*b^7 - 82*a^12*b^9 + 264*a^10*b^11 + 282*a^8*b^13 + 64*a^6*b^15 - 33*a^4*b^17 - 12*a^2*b^19 + b^21)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 105*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 2*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^4 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 + (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 105*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 2*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d - 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^4 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 + (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((3*a^14*b - 91*a^12*b^3 + 795*a^10*b^5 - 1611*a^8*b^7 + 1217*a^6*b^9 - 345*a^4*b^11 + 33*a^2*b^13 - b^15)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - (a^21 - 30*a^19*b^2 + 249*a^17*b^4 - 280*a^15*b^6 - 1038*a^13*b^8 + 732*a^11*b^10 + 1322*a^9*b^12 - 504*a^7*b^14 - 531*a^5*b^16 + 82*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 + 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) + 8*(5*(10*a^15 + 39*a^13*b^2 + 24*a^11*b^4 - 115*a^9*b^6 - 270*a^7*b^8 - 255*a^5*b^10 - 116*a^3*b^12 - 21*a*b^14)*cos(d*x + c)^4 - 35*(a^15 + 3*a^13*b^2 - 3*a^11*b^4 - 25*a^9*b^6 - 45*a^7*b^8 - 39*a^5*b^10 - 17*a^3*b^12 - 3*a*b^14)*cos(d*x + c)^2 + 21*((18*a^14*b + 103*a^12*b^3 + 240*a^10*b^5 + 285*a^8*b^7 + 170*a^6*b^9 + 33*a^4*b^11 - 12*a^2*b^13 - 5*b^15)*cos(d*x + c)^3 - 5*(3*a^14*b + 17*a^12*b^3 + 39*a^10*b^5 + 45*a^8*b^7 + 25*a^6*b^9 + 3*a^4*b^11 - 3*a^2*b^13 - b^15)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 - 2*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d)","B",0
577,1,8178,0,2.774696," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{1260 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{6} - 3 \, d^{5} \cos\left(d x + c\right)^{4} + 3 \, d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(-\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 1260 \, \sqrt{2} {\left(d^{5} \cos\left(d x + c\right)^{6} - 3 \, d^{5} \cos\left(d x + c\right)^{4} + 3 \, d^{5} \cos\left(d x + c\right)^{2} - d^{5}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} \arctan\left(\frac{{\left(a^{24} - 6 \, a^{22} b^{2} - 84 \, a^{20} b^{4} - 322 \, a^{18} b^{6} - 603 \, a^{16} b^{8} - 540 \, a^{14} b^{10} + 540 \, a^{10} b^{14} + 603 \, a^{8} b^{16} + 322 \, a^{6} b^{18} + 84 \, a^{4} b^{20} + 6 \, a^{2} b^{22} - b^{24}\right)} d^{4} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} - \sqrt{2} {\left({\left(3 \, a^{2} b - b^{3}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(3 \, a^{14} b - 37 \, a^{12} b^{3} - 69 \, a^{10} b^{5} + 27 \, a^{8} b^{7} + 81 \, a^{6} b^{9} + 9 \, a^{4} b^{11} - 15 \, a^{2} b^{13} + b^{15}\right)} d^{7} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}} + {\left(a^{21} - 12 \, a^{19} b^{2} - 33 \, a^{17} b^{4} + 64 \, a^{15} b^{6} + 282 \, a^{13} b^{8} + 264 \, a^{11} b^{10} - 82 \, a^{9} b^{12} - 288 \, a^{7} b^{14} - 171 \, a^{5} b^{16} - 28 \, a^{3} b^{18} + 3 \, a b^{20}\right)} d^{5} \sqrt{\frac{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{3}{4}}}{a^{36} - 18 \, a^{34} b^{2} - 39 \, a^{32} b^{4} + 848 \, a^{30} b^{6} + 5556 \, a^{28} b^{8} + 15240 \, a^{26} b^{10} + 20420 \, a^{24} b^{12} + 5424 \, a^{22} b^{14} - 25938 \, a^{20} b^{16} - 42988 \, a^{18} b^{18} - 25938 \, a^{16} b^{20} + 5424 \, a^{14} b^{22} + 20420 \, a^{12} b^{24} + 15240 \, a^{10} b^{26} + 5556 \, a^{8} b^{28} + 848 \, a^{6} b^{30} - 39 \, a^{4} b^{32} - 18 \, a^{2} b^{34} + b^{36}}\right) + 315 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d + 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{6} - 3 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 315 \, \sqrt{2} {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d + 2 \, {\left({\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{6} - 3 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{3}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{18} - 27 \, a^{16} b^{2} + 168 \, a^{14} b^{4} + 224 \, a^{12} b^{6} - 366 \, a^{10} b^{8} - 366 \, a^{8} b^{10} + 224 \, a^{6} b^{12} + 168 \, a^{4} b^{14} - 27 \, a^{2} b^{16} + b^{18}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{15} - 33 \, a^{13} b^{2} + 345 \, a^{11} b^{4} - 1217 \, a^{9} b^{6} + 1611 \, a^{7} b^{8} - 795 \, a^{5} b^{10} + 91 \, a^{3} b^{12} - 3 \, a b^{14}\right)} d^{3} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}} \cos\left(d x + c\right) + {\left(3 \, a^{20} b - 82 \, a^{18} b^{3} + 531 \, a^{16} b^{5} + 504 \, a^{14} b^{7} - 1322 \, a^{12} b^{9} - 732 \, a^{10} b^{11} + 1038 \, a^{8} b^{13} + 280 \, a^{6} b^{15} - 249 \, a^{4} b^{17} + 30 \, a^{2} b^{19} - b^{21}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12} - 2 \, {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} d^{2} \sqrt{\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}}}{a^{12} - 30 \, a^{10} b^{2} + 255 \, a^{8} b^{4} - 452 \, a^{6} b^{6} + 255 \, a^{4} b^{8} - 30 \, a^{2} b^{10} + b^{12}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{24} - 24 \, a^{22} b^{2} + 90 \, a^{20} b^{4} + 648 \, a^{18} b^{6} + 783 \, a^{16} b^{8} - 624 \, a^{14} b^{10} - 1748 \, a^{12} b^{12} - 624 \, a^{10} b^{14} + 783 \, a^{8} b^{16} + 648 \, a^{6} b^{18} + 90 \, a^{4} b^{20} - 24 \, a^{2} b^{22} + b^{24}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(15 \, {\left(30 \, a^{14} b + 173 \, a^{12} b^{3} + 408 \, a^{10} b^{5} + 495 \, a^{8} b^{7} + 310 \, a^{6} b^{9} + 75 \, a^{4} b^{11} - 12 \, a^{2} b^{13} - 7 \, b^{15}\right)} \cos\left(d x + c\right)^{6} - 15 \, {\left(51 \, a^{14} b + 292 \, a^{12} b^{3} + 681 \, a^{10} b^{5} + 810 \, a^{8} b^{7} + 485 \, a^{6} b^{9} + 96 \, a^{4} b^{11} - 33 \, a^{2} b^{13} - 14 \, b^{15}\right)} \cos\left(d x + c\right)^{4} + 105 \, {\left(3 \, a^{14} b + 17 \, a^{12} b^{3} + 39 \, a^{10} b^{5} + 45 \, a^{8} b^{7} + 25 \, a^{6} b^{9} + 3 \, a^{4} b^{11} - 3 \, a^{2} b^{13} - b^{15}\right)} \cos\left(d x + c\right)^{2} - 7 \, {\left({\left(59 \, a^{15} + 192 \, a^{13} b^{2} - 87 \, a^{11} b^{4} - 1250 \, a^{9} b^{6} - 2355 \, a^{7} b^{8} - 2076 \, a^{5} b^{10} - 913 \, a^{3} b^{12} - 162 \, a b^{14}\right)} \cos\left(d x + c\right)^{5} - 99 \, {\left(a^{15} + 3 \, a^{13} b^{2} - 3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 45 \, a^{7} b^{8} - 39 \, a^{5} b^{10} - 17 \, a^{3} b^{12} - 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{3} + 45 \, {\left(a^{15} + 3 \, a^{13} b^{2} - 3 \, a^{11} b^{4} - 25 \, a^{9} b^{6} - 45 \, a^{7} b^{8} - 39 \, a^{5} b^{10} - 17 \, a^{3} b^{12} - 3 \, a b^{14}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{1260 \, {\left({\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"1/1260*(1260*sqrt(2)*(d^5*cos(d*x + c)^6 - 3*d^5*cos(d*x + c)^4 + 3*d^5*cos(d*x + c)^2 - d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(-((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) + sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 1260*sqrt(2)*(d^5*cos(d*x + c)^6 - 3*d^5*cos(d*x + c)^4 + 3*d^5*cos(d*x + c)^2 - d^5)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4)*arctan(((a^24 - 6*a^22*b^2 - 84*a^20*b^4 - 322*a^18*b^6 - 603*a^16*b^8 - 540*a^14*b^10 + 540*a^10*b^14 + 603*a^8*b^16 + 322*a^6*b^18 + 84*a^4*b^20 + 6*a^2*b^22 - b^24)*d^4*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) - sqrt(2)*((3*a^2*b - b^3)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4) - sqrt(2)*((3*a^14*b - 37*a^12*b^3 - 69*a^10*b^5 + 27*a^8*b^7 + 81*a^6*b^9 + 9*a^4*b^11 - 15*a^2*b^13 + b^15)*d^7*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4) + (a^21 - 12*a^19*b^2 - 33*a^17*b^4 + 64*a^15*b^6 + 282*a^13*b^8 + 264*a^11*b^10 - 82*a^9*b^12 - 288*a^7*b^14 - 171*a^5*b^16 - 28*a^3*b^18 + 3*a*b^20)*d^5*sqrt((a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(3/4))/(a^36 - 18*a^34*b^2 - 39*a^32*b^4 + 848*a^30*b^6 + 5556*a^28*b^8 + 15240*a^26*b^10 + 20420*a^24*b^12 + 5424*a^22*b^14 - 25938*a^20*b^16 - 42988*a^18*b^18 - 25938*a^16*b^20 + 5424*a^14*b^22 + 20420*a^12*b^24 + 15240*a^10*b^26 + 5556*a^8*b^28 + 848*a^6*b^30 - 39*a^4*b^32 - 18*a^2*b^34 + b^36)) + 315*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^6 - 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 + 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d + 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^6 - 3*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^4 + 3*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 - (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 315*sqrt(2)*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^6 - 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 + 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d + 2*((3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^6 - 3*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^4 + 3*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3*cos(d*x + c)^2 - (3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^3)*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4)*log(((a^18 - 27*a^16*b^2 + 168*a^14*b^4 + 224*a^12*b^6 - 366*a^10*b^8 - 366*a^8*b^10 + 224*a^6*b^12 + 168*a^4*b^14 - 27*a^2*b^16 + b^18)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) - sqrt(2)*((a^15 - 33*a^13*b^2 + 345*a^11*b^4 - 1217*a^9*b^6 + 1611*a^7*b^8 - 795*a^5*b^10 + 91*a^3*b^12 - 3*a*b^14)*d^3*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)*cos(d*x + c) + (3*a^20*b - 82*a^18*b^3 + 531*a^16*b^5 + 504*a^14*b^7 - 1322*a^12*b^9 - 732*a^10*b^11 + 1038*a^8*b^13 + 280*a^6*b^15 - 249*a^4*b^17 + 30*a^2*b^19 - b^21)*d*cos(d*x + c))*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12 - 2*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*d^2*sqrt((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4))/(a^12 - 30*a^10*b^2 + 255*a^8*b^4 - 452*a^6*b^6 + 255*a^4*b^8 - 30*a^2*b^10 + b^12))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)/d^4)^(1/4) + (a^24 - 24*a^22*b^2 + 90*a^20*b^4 + 648*a^18*b^6 + 783*a^16*b^8 - 624*a^14*b^10 - 1748*a^12*b^12 - 624*a^10*b^14 + 783*a^8*b^16 + 648*a^6*b^18 + 90*a^4*b^20 - 24*a^2*b^22 + b^24)*sin(d*x + c))/cos(d*x + c)) - 8*(15*(30*a^14*b + 173*a^12*b^3 + 408*a^10*b^5 + 495*a^8*b^7 + 310*a^6*b^9 + 75*a^4*b^11 - 12*a^2*b^13 - 7*b^15)*cos(d*x + c)^6 - 15*(51*a^14*b + 292*a^12*b^3 + 681*a^10*b^5 + 810*a^8*b^7 + 485*a^6*b^9 + 96*a^4*b^11 - 33*a^2*b^13 - 14*b^15)*cos(d*x + c)^4 + 105*(3*a^14*b + 17*a^12*b^3 + 39*a^10*b^5 + 45*a^8*b^7 + 25*a^6*b^9 + 3*a^4*b^11 - 3*a^2*b^13 - b^15)*cos(d*x + c)^2 - 7*((59*a^15 + 192*a^13*b^2 - 87*a^11*b^4 - 1250*a^9*b^6 - 2355*a^7*b^8 - 2076*a^5*b^10 - 913*a^3*b^12 - 162*a*b^14)*cos(d*x + c)^5 - 99*(a^15 + 3*a^13*b^2 - 3*a^11*b^4 - 25*a^9*b^6 - 45*a^7*b^8 - 39*a^5*b^10 - 17*a^3*b^12 - 3*a*b^14)*cos(d*x + c)^3 + 45*(a^15 + 3*a^13*b^2 - 3*a^11*b^4 - 25*a^9*b^6 - 45*a^7*b^8 - 39*a^5*b^10 - 17*a^3*b^12 - 3*a*b^14)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^6 - 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^4 + 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d*cos(d*x + c)^2 - (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*d)","B",0
578,1,2640,0,0.537554," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{4} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} d^{4} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + \sqrt{2} {\left(2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/4*(4*sqrt(2)*d^4*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*d^4*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + sqrt(2)*(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt((2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) + (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
579,1,2694,0,0.526293," ","integrate((a+b*tan(d*x+c))/(-tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} d^{4} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} d^{4} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - \sqrt{2} {\left(a d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{2} b + b^{3}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4}}}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + \sqrt{2} {\left(2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right)\right)} \sqrt{-\frac{2 \, a b d^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4}}\right)^{\frac{1}{4}} - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-1/4*(4*sqrt(2)*d^4*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(-sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) - (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) + sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(-sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*d^4*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) - sqrt(2)*(a*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^2*b + b^3)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(-sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) - (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4) - sqrt(2)*((a^5 - a*b^4)*d^7*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4) + (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/d^4))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(-sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + sqrt(2)*(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(-sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) - (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) + a^4 + 2*a^2*b^2 + b^4)*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4)*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*cos(d*x + c))*sqrt(-(2*a*b*d^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/d^4) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(-sin(d*x + c)/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/d^4)^(1/4) - (a^8 - 2*a^4*b^4 + b^8)*sin(d*x + c))/cos(d*x + c)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
580,1,2884,0,0.557038," ","integrate((a+b*tan(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} d^{4} e^{2} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - {\left(a^{2} b + b^{3}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} d^{4} e^{2} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - {\left(a^{2} b + b^{3}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + \sqrt{2} {\left(2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}\right)}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/4*(4*sqrt(2)*d^4*e^2*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2))*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) + sqrt(2)*((a^5 - a*b^4)*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt(e*sin(d*x + c)/cos(d*x + c))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4) + sqrt(2)*(a*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) - (a^2*b + b^3)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(e*sin(d*x + c)/cos(d*x + c))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*d^4*e^2*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2))*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) - sqrt(2)*((a^5 - a*b^4)*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt(e*sin(d*x + c)/cos(d*x + c))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4) - sqrt(2)*(a*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) - (a^2*b + b^3)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(e*sin(d*x + c)/cos(d*x + c))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + sqrt(2)*(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(e*sin(d*x + c)/cos(d*x + c))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c)) - sqrt(2)*(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(e*sin(d*x + c)/cos(d*x + c))*sqrt((2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
581,1,2938,0,0.539398," ","integrate((a+b*tan(d*x+c))/(-e*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} d^{4} e^{2} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{-\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(a d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + {\left(a^{2} b + b^{3}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{-\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + 4 \, \sqrt{2} d^{4} e^{2} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - \sqrt{2} {\left({\left(a^{5} - a b^{4}\right)} d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{-\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(a d^{7} e^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + {\left(a^{2} b + b^{3}\right)} d^{5} e^{2} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}}\right)} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{-\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{3}{4}}}{a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}}\right) + \sqrt{2} {\left(2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{-\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} + a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) - {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} e \sin\left(d x + c\right) - \sqrt{2} {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} e^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} \cos\left(d x + c\right) + {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d e \cos\left(d x + c\right)\right)} \sqrt{-\frac{e \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sqrt{-\frac{2 \, a b d^{2} e \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}} - a^{4} - 2 \, a^{2} b^{2} - b^{4}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{d^{4} e^{2}}\right)^{\frac{1}{4}}}{\cos\left(d x + c\right)}\right)}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-1/4*(4*sqrt(2)*d^4*e^2*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2))*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) + sqrt(2)*((a^5 - a*b^4)*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) + (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt(-e*sin(d*x + c)/cos(d*x + c))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4) + sqrt(2)*(a*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) + (a^2*b + b^3)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(-e*sin(d*x + c)/cos(d*x + c))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + 4*sqrt(2)*d^4*e^2*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4)*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2))*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) - sqrt(2)*((a^5 - a*b^4)*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) + (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt(-e*sin(d*x + c)/cos(d*x + c))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4) - sqrt(2)*(a*d^7*e^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)) + (a^2*b + b^3)*d^5*e^2*sqrt((a^4 - 2*a^2*b^2 + b^4)/(d^4*e^2)))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(-e*sin(d*x + c)/cos(d*x + c))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(3/4))/(a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)) + sqrt(2)*(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) + sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(-e*sin(d*x + c)/cos(d*x + c))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c)) - sqrt(2)*(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) + a^4 + 2*a^2*b^2 + b^4)*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) - (a^8 - 2*a^4*b^4 + b^8)*e*sin(d*x + c) - sqrt(2)*((a^4*b - 2*a^2*b^3 + b^5)*d^3*e^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))*cos(d*x + c) + (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*e*cos(d*x + c))*sqrt(-e*sin(d*x + c)/cos(d*x + c))*sqrt(-(2*a*b*d^2*e*sqrt((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2)) - a^4 - 2*a^2*b^2 - b^4)/(a^4 - 2*a^2*b^2 + b^4))*((a^4 + 2*a^2*b^2 + b^4)/(d^4*e^2))^(1/4))/cos(d*x + c)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
582,1,7470,0,11.143595," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{60 \, \sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{2} - 30 \, a^{4} \sqrt{-\frac{a}{b}} \cos\left(d x + c\right)^{2} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 15 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 15 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{2} b^{2} + 3 \, b^{4} + 3 \, {\left(5 \, a^{4} - a^{2} b^{2} - 6 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{60 \, \sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{2} + 60 \, \sqrt{2} {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right)^{2} + 120 \, a^{4} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) \cos\left(d x + c\right)^{2} - 15 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 15 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right)^{2} - {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, a^{2} b^{2} + 3 \, b^{4} + 3 \, {\left(5 \, a^{4} - a^{2} b^{2} - 6 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 5 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[-1/60*(60*sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c)^2 + 60*sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c)^2 - 30*a^4*sqrt(-a/b)*cos(d*x + c)^2*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 15*sqrt(2)*(2*(a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c)^2 - (a^2*b^3 + b^5)*d*cos(d*x + c)^2)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 15*sqrt(2)*(2*(a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c)^2 - (a^2*b^3 + b^5)*d*cos(d*x + c)^2)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 8*(3*a^2*b^2 + 3*b^4 + 3*(5*a^4 - a^2*b^2 - 6*b^4)*cos(d*x + c)^2 - 5*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^2*b^3 + b^5)*d*cos(d*x + c)^2), -1/60*(60*sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c)^2 + 60*sqrt(2)*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c)^2 + 120*a^4*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a)*cos(d*x + c)^2 - 15*sqrt(2)*(2*(a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c)^2 - (a^2*b^3 + b^5)*d*cos(d*x + c)^2)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 15*sqrt(2)*(2*(a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c)^2 - (a^2*b^3 + b^5)*d*cos(d*x + c)^2)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 8*(3*a^2*b^2 + 3*b^4 + 3*(5*a^4 - a^2*b^2 - 6*b^4)*cos(d*x + c)^2 - 5*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^2*b^3 + b^5)*d*cos(d*x + c)^2)]","B",0
583,1,7356,0,11.321812," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{2} {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right) + 6 \, a^{3} \sqrt{-\frac{a}{b}} \cos\left(d x + c\right) \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 3 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}, \frac{12 \, \sqrt{2} {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) \cos\left(d x + c\right) + 24 \, a^{3} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left(2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(3 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left(a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/12*(12*sqrt(2)*(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c) + 12*sqrt(2)*(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c) + 6*a^3*sqrt(-a/b)*cos(d*x + c)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 3*sqrt(2)*(2*(a^3*b^3 + a*b^5)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^2*b^2 + b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(2*(a^3*b^3 + a*b^5)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^2*b^2 + b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 8*(3*(a^3 + a*b^2)*cos(d*x + c) - (a^2*b + b^3)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^2*b^2 + b^4)*d*cos(d*x + c)), 1/12*(12*sqrt(2)*(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c) + 12*sqrt(2)*(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4))*cos(d*x + c) + 24*a^3*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a)*cos(d*x + c) + 3*sqrt(2)*(2*(a^3*b^3 + a*b^5)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^2*b^2 + b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(2*(a^3*b^3 + a*b^5)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^2*b^2 + b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 8*(3*(a^3 + a*b^2)*cos(d*x + c) - (a^2*b + b^3)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^2*b^2 + b^4)*d*cos(d*x + c))]","B",0
584,1,7198,0,11.826932," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 2 \, a^{2} \sqrt{-\frac{a}{b}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} b + b^{3}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} b + b^{3}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{2} + b^{2}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} b + b^{3}\right)} d}, \frac{4 \, \sqrt{2} {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) - 8 \, a^{2} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} b + b^{3}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} b + b^{3}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(a^{2} + b^{2}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} b + b^{3}\right)} d}\right]"," ",0,"[1/4*(4*sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 2*a^2*sqrt(-a/b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - sqrt(2)*(2*(a^3*b^2 + a*b^4)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2*b + b^3)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(a^3*b^2 + a*b^4)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2*b + b^3)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 8*(a^2 + b^2)*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^2*b + b^3)*d), 1/4*(4*sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) - 8*a^2*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) - sqrt(2)*(2*(a^3*b^2 + a*b^4)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2*b + b^3)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(a^3*b^2 + a*b^4)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2*b + b^3)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 8*(a^2 + b^2)*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^2*b + b^3)*d)]","B",0
585,1,7094,0,11.032277," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 2 \, a \sqrt{-\frac{a}{b}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}, -\frac{4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, a \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}\right]"," ",0,"[-1/4*(4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 2*a*sqrt(-a/b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^2 + b^2)*d), -1/4*(4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 8*a*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a))/((a^2 + b^2)*d)]","B",0
586,1,7205,0,11.001442," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 2 \, \sqrt{-a b} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a \cos\left(d x + c\right)^{2} - b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-a b} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}, -\frac{4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, \sqrt{a b} \arctan\left(\frac{{\left(2 \, a b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{3} + b^{2} \cos\left(d x + c\right)\right)} \sqrt{a b} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}\right]"," ",0,"[-1/4*(4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) - sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 2*sqrt(-a*b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a*cos(d*x + c)^2 - b*cos(d*x + c)*sin(d*x + c))*sqrt(-a*b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^2 + b^2)*d), -1/4*(4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) - sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 8*sqrt(a*b)*arctan((2*a*b*cos(d*x + c)^2*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^3 + b^2*cos(d*x + c))*sqrt(a*b)*sqrt(sin(d*x + c)/cos(d*x + c))/(2*a*b^2*cos(d*x + c)^3 - 2*a*b^2*cos(d*x + c) - (b^3 + (a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))))/((a^2 + b^2)*d)]","B",0
587,1,7202,0,11.298349," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 2 \, b \sqrt{-\frac{b}{a}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}, \frac{4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{5} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{2} + b^{2}\right)} d\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, b \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(2 \, a^{2} b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} + b^{2}\right)} d}\right]"," ",0,"[1/4*(4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 2*b*sqrt(-b/a)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a^2*cos(d*x + c)^2 - a*b*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^2 + b^2)*d), 1/4*(4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^5*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*(2*(a^3*b + a*b^3)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^2 + b^2)*d)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 8*b*sqrt(b/a)*arctan((2*a^2*b*cos(d*x + c)^2*sin(d*x + c) + a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sqrt(b/a)*sqrt(sin(d*x + c)/cos(d*x + c))/(2*a*b^2*cos(d*x + c)^3 - 2*a*b^2*cos(d*x + c) - (b^3 + (a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))))/((a^2 + b^2)*d)]","B",0
588,1,7748,0,10.887960," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 8 \, {\left(a^{2} + b^{2}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} b + a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} b + a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 2 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{4 \, {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 4 \, \sqrt{2} {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 8 \, {\left(a^{2} + b^{2}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} b + a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{4} b + a^{2} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 8 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(2 \, a^{2} b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right)}{4 \, {\left({\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 8*(a^2 + b^2)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - 2*((a^4*b + a^2*b^3)*d^3*cos(d*x + c)^2 - (a^4*b + a^2*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - 2*((a^4*b + a^2*b^3)*d^3*cos(d*x + c)^2 - (a^4*b + a^2*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 2*(b^2*cos(d*x + c)^2 - b^2)*sqrt(-b/a)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a^2*cos(d*x + c)^2 - a*b*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d), 1/4*(4*sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 4*sqrt(2)*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*cos(d*x + c)^2 - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 8*(a^2 + b^2)*sqrt(sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - 2*((a^4*b + a^2*b^3)*d^3*cos(d*x + c)^2 - (a^4*b + a^2*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d - 2*((a^4*b + a^2*b^3)*d^3*cos(d*x + c)^2 - (a^4*b + a^2*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 8*(b^2*cos(d*x + c)^2 - b^2)*sqrt(b/a)*arctan((2*a^2*b*cos(d*x + c)^2*sin(d*x + c) + a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sqrt(b/a)*sqrt(sin(d*x + c)/cos(d*x + c))/(2*a*b^2*cos(d*x + c)^3 - 2*a*b^2*cos(d*x + c) - (b^3 + (a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))))/((a^3 + a*b^2)*d*cos(d*x + c)^2 - (a^3 + a*b^2)*d)]","B",0
589,1,7820,0,11.379551," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{12 \, \sqrt{2} {\left({\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 12 \, \sqrt{2} {\left({\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 3 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + 2 \, {\left({\left(a^{5} b + a^{3} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} b + a^{3} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + 2 \, {\left({\left(a^{5} b + a^{3} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} b + a^{3} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 6 \, {\left(b^{3} \cos\left(d x + c\right)^{2} - b^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 8 \, {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d\right)}}, -\frac{12 \, \sqrt{2} {\left({\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 12 \, \sqrt{2} {\left({\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} - {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{11} + 3 \, a^{9} b^{2} + 2 \, a^{7} b^{4} - 2 \, a^{5} b^{6} - 3 \, a^{3} b^{8} - a b^{10}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + {\left(a^{8} b + 2 \, a^{6} b^{3} - 2 \, a^{2} b^{7} - b^{9}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 3 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + 2 \, {\left({\left(a^{5} b + a^{3} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} b + a^{3} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d + 2 \, {\left({\left(a^{5} b + a^{3} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} - {\left(a^{5} b + a^{3} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 24 \, {\left(b^{3} \cos\left(d x + c\right)^{2} - b^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(2 \, a^{2} b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right) - 8 \, {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d\right)}}\right]"," ",0,"[-1/12*(12*sqrt(2)*((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5*cos(d*x + c)^2 - (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 12*sqrt(2)*((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5*cos(d*x + c)^2 - (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 3*sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + 2*((a^5*b + a^3*b^3)*d^3*cos(d*x + c)^2 - (a^5*b + a^3*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + 2*((a^5*b + a^3*b^3)*d^3*cos(d*x + c)^2 - (a^5*b + a^3*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 6*(b^3*cos(d*x + c)^2 - b^3)*sqrt(-b/a)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a^2*cos(d*x + c)^2 - a*b*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 8*((a^3 + a*b^2)*cos(d*x + c)^2 - 3*(a^2*b + b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d), -1/12*(12*sqrt(2)*((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5*cos(d*x + c)^2 - (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 12*sqrt(2)*((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5*cos(d*x + c)^2 - (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^11 + 3*a^9*b^2 + 2*a^7*b^4 - 2*a^5*b^6 - 3*a^3*b^8 - a*b^10)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + (a^8*b + 2*a^6*b^3 - 2*a^2*b^7 - b^9)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 3*sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + 2*((a^5*b + a^3*b^3)*d^3*cos(d*x + c)^2 - (a^5*b + a^3*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d + 2*((a^5*b + a^3*b^3)*d^3*cos(d*x + c)^2 - (a^5*b + a^3*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 24*(b^3*cos(d*x + c)^2 - b^3)*sqrt(b/a)*arctan((2*a^2*b*cos(d*x + c)^2*sin(d*x + c) + a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sqrt(b/a)*sqrt(sin(d*x + c)/cos(d*x + c))/(2*a*b^2*cos(d*x + c)^3 - 2*a*b^2*cos(d*x + c) - (b^3 + (a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))) - 8*((a^3 + a*b^2)*cos(d*x + c)^2 - 3*(a^2*b + b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^4 + a^2*b^2)*d*cos(d*x + c)^2 - (a^4 + a^2*b^2)*d)]","B",0
590,1,8348,0,11.484127," ","integrate(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{60 \, \sqrt{2} {\left({\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 60 \, \sqrt{2} {\left({\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 15 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d - 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{6} b + a^{4} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d - 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{6} b + a^{4} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 30 \, {\left(b^{4} \cos\left(d x + c\right)^{4} - 2 \, b^{4} \cos\left(d x + c\right)^{2} + b^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 8 \, {\left(5 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(6 \, a^{4} + a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d\right)}}, -\frac{60 \, \sqrt{2} {\left({\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 60 \, \sqrt{2} {\left({\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5} \cos\left(d x + c\right)^{2} + {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{5}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{4} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{10} b + 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} - 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} - b^{11}\right)} d^{7} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} - {\left(a^{9} + 2 \, a^{7} b^{2} - 2 \, a^{3} b^{6} - a b^{8}\right)} d^{5} \sqrt{\frac{a^{4} - 2 \, a^{2} b^{2} + b^{4}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}\right) + 15 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d - 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{6} b + a^{4} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 15 \, \sqrt{2} {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d - 2 \, {\left({\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + a^{4} b^{3}\right)} d^{3} \cos\left(d x + c\right)^{2} + {\left(a^{6} b + a^{4} b^{3}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}} \cos\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}}}{a^{4} - 2 \, a^{2} b^{2} + b^{4}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 120 \, {\left(b^{4} \cos\left(d x + c\right)^{4} - 2 \, b^{4} \cos\left(d x + c\right)^{2} + b^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(2 \, a^{2} b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right) + 8 \, {\left(5 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(6 \, a^{4} + a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{3} - 5 \, {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{60 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[-1/60*(60*sqrt(2)*((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^4 - 2*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^2 + (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 60*sqrt(2)*((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^4 - 2*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^2 + (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 15*sqrt(2)*((a^5 + a^3*b^2)*d*cos(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cos(d*x + c)^2 + (a^5 + a^3*b^2)*d - 2*((a^6*b + a^4*b^3)*d^3*cos(d*x + c)^4 - 2*(a^6*b + a^4*b^3)*d^3*cos(d*x + c)^2 + (a^6*b + a^4*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*((a^5 + a^3*b^2)*d*cos(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cos(d*x + c)^2 + (a^5 + a^3*b^2)*d - 2*((a^6*b + a^4*b^3)*d^3*cos(d*x + c)^4 - 2*(a^6*b + a^4*b^3)*d^3*cos(d*x + c)^2 + (a^6*b + a^4*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 30*(b^4*cos(d*x + c)^4 - 2*b^4*cos(d*x + c)^2 + b^4)*sqrt(-b/a)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a^2*cos(d*x + c)^2 - a*b*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 8*(5*(a^3*b + a*b^3)*cos(d*x + c)^4 - 5*(a^3*b + a*b^3)*cos(d*x + c)^2 + 3*((6*a^4 + a^2*b^2 - 5*b^4)*cos(d*x + c)^3 - 5*(a^4 - b^4)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^5 + a^3*b^2)*d*cos(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cos(d*x + c)^2 + (a^5 + a^3*b^2)*d), -1/60*(60*sqrt(2)*((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^4 - 2*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^2 + (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(-((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) - sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 60*sqrt(2)*((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^4 - 2*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5*cos(d*x + c)^2 + (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^5)*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4)*arctan(((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^4*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) + sqrt(2)*((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4) + sqrt(2)*((a^10*b + 3*a^8*b^3 + 2*a^6*b^5 - 2*a^4*b^7 - 3*a^2*b^9 - b^11)*d^7*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)) - (a^9 + 2*a^7*b^2 - 2*a^3*b^6 - a*b^8)*d^5*sqrt((a^4 - 2*a^2*b^2 + b^4)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(3/4))/(a^4 - 2*a^2*b^2 + b^4)) + 15*sqrt(2)*((a^5 + a^3*b^2)*d*cos(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cos(d*x + c)^2 + (a^5 + a^3*b^2)*d - 2*((a^6*b + a^4*b^3)*d^3*cos(d*x + c)^4 - 2*(a^6*b + a^4*b^3)*d^3*cos(d*x + c)^2 + (a^6*b + a^4*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) + sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) - 15*sqrt(2)*((a^5 + a^3*b^2)*d*cos(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cos(d*x + c)^2 + (a^5 + a^3*b^2)*d - 2*((a^6*b + a^4*b^3)*d^3*cos(d*x + c)^4 - 2*(a^6*b + a^4*b^3)*d^3*cos(d*x + c)^2 + (a^6*b + a^4*b^3)*d^3)*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4)*log(((a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - sqrt(2)*((a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))*cos(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))*sqrt((a^4 + 2*a^2*b^2 + b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d^2*sqrt(1/((a^4 + 2*a^2*b^2 + b^4)*d^4)))/(a^4 - 2*a^2*b^2 + b^4))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^4 + 2*a^2*b^2 + b^4)*d^4))^(1/4) + (a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/cos(d*x + c)) + 120*(b^4*cos(d*x + c)^4 - 2*b^4*cos(d*x + c)^2 + b^4)*sqrt(b/a)*arctan((2*a^2*b*cos(d*x + c)^2*sin(d*x + c) + a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sqrt(b/a)*sqrt(sin(d*x + c)/cos(d*x + c))/(2*a*b^2*cos(d*x + c)^3 - 2*a*b^2*cos(d*x + c) - (b^3 + (a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))) + 8*(5*(a^3*b + a*b^3)*cos(d*x + c)^4 - 5*(a^3*b + a*b^3)*cos(d*x + c)^2 + 3*((6*a^4 + a^2*b^2 - 5*b^4)*cos(d*x + c)^3 - 5*(a^4 - b^4)*cos(d*x + c))*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^5 + a^3*b^2)*d*cos(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cos(d*x + c)^2 + (a^5 + a^3*b^2)*d)]","B",0
591,1,14604,0,13.002531," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{2} {\left({\left(a^{14} b^{3} + 5 \, a^{12} b^{5} + 9 \, a^{10} b^{7} + 5 \, a^{8} b^{9} - 5 \, a^{6} b^{11} - 9 \, a^{4} b^{13} - 5 \, a^{2} b^{15} - b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{13} b^{4} + 6 \, a^{11} b^{6} + 15 \, a^{9} b^{8} + 20 \, a^{7} b^{10} + 15 \, a^{5} b^{12} + 6 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{12} b^{5} + 6 \, a^{10} b^{7} + 15 \, a^{8} b^{9} + 20 \, a^{6} b^{11} + 15 \, a^{4} b^{13} + 6 \, a^{2} b^{15} + b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 12 \, \sqrt{2} {\left({\left(a^{14} b^{3} + 5 \, a^{12} b^{5} + 9 \, a^{10} b^{7} + 5 \, a^{8} b^{9} - 5 \, a^{6} b^{11} - 9 \, a^{4} b^{13} - 5 \, a^{2} b^{15} - b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{13} b^{4} + 6 \, a^{11} b^{6} + 15 \, a^{9} b^{8} + 20 \, a^{7} b^{10} + 15 \, a^{5} b^{12} + 6 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{12} b^{5} + 6 \, a^{10} b^{7} + 15 \, a^{8} b^{9} + 20 \, a^{6} b^{11} + 15 \, a^{4} b^{13} + 6 \, a^{2} b^{15} + b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) - 3 \, \sqrt{2} {\left({\left(a^{6} b^{3} + a^{4} b^{5} - a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) - 4 \, {\left({\left(a^{9} b^{4} - 2 \, a^{5} b^{8} + a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b^{5} + a^{6} b^{7} - a^{4} b^{9} - a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{7} b^{6} + a^{5} b^{8} - a^{3} b^{10} - a b^{12}\right)} d^{3} \cos\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{6} b^{3} + a^{4} b^{5} - a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) - 4 \, {\left({\left(a^{9} b^{4} - 2 \, a^{5} b^{8} + a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b^{5} + a^{6} b^{7} - a^{4} b^{9} - a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{7} b^{6} + a^{5} b^{8} - a^{3} b^{10} - a b^{12}\right)} d^{3} \cos\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, {\left({\left(5 \, a^{7} + 4 \, a^{5} b^{2} - 9 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{6} b + 9 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(5 \, a^{5} b^{2} + 9 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 4 \, {\left({\left(15 \, a^{7} + 19 \, a^{5} b^{2} - 4 \, a^{3} b^{4} - 8 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 2 \, b^{7} - {\left(25 \, a^{6} b + 49 \, a^{4} b^{3} + 26 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{6} b^{3} + a^{4} b^{5} - a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)\right)}}, \frac{12 \, \sqrt{2} {\left({\left(a^{14} b^{3} + 5 \, a^{12} b^{5} + 9 \, a^{10} b^{7} + 5 \, a^{8} b^{9} - 5 \, a^{6} b^{11} - 9 \, a^{4} b^{13} - 5 \, a^{2} b^{15} - b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{13} b^{4} + 6 \, a^{11} b^{6} + 15 \, a^{9} b^{8} + 20 \, a^{7} b^{10} + 15 \, a^{5} b^{12} + 6 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{12} b^{5} + 6 \, a^{10} b^{7} + 15 \, a^{8} b^{9} + 20 \, a^{6} b^{11} + 15 \, a^{4} b^{13} + 6 \, a^{2} b^{15} + b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 12 \, \sqrt{2} {\left({\left(a^{14} b^{3} + 5 \, a^{12} b^{5} + 9 \, a^{10} b^{7} + 5 \, a^{8} b^{9} - 5 \, a^{6} b^{11} - 9 \, a^{4} b^{13} - 5 \, a^{2} b^{15} - b^{17}\right)} d^{5} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{13} b^{4} + 6 \, a^{11} b^{6} + 15 \, a^{9} b^{8} + 20 \, a^{7} b^{10} + 15 \, a^{5} b^{12} + 6 \, a^{3} b^{14} + a b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{12} b^{5} + 6 \, a^{10} b^{7} + 15 \, a^{8} b^{9} + 20 \, a^{6} b^{11} + 15 \, a^{4} b^{13} + 6 \, a^{2} b^{15} + b^{17}\right)} d^{5} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) - 3 \, \sqrt{2} {\left({\left(a^{6} b^{3} + a^{4} b^{5} - a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) - 4 \, {\left({\left(a^{9} b^{4} - 2 \, a^{5} b^{8} + a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b^{5} + a^{6} b^{7} - a^{4} b^{9} - a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{7} b^{6} + a^{5} b^{8} - a^{3} b^{10} - a b^{12}\right)} d^{3} \cos\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, \sqrt{2} {\left({\left(a^{6} b^{3} + a^{4} b^{5} - a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) - 4 \, {\left({\left(a^{9} b^{4} - 2 \, a^{5} b^{8} + a b^{12}\right)} d^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b^{5} + a^{6} b^{7} - a^{4} b^{9} - a^{2} b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{7} b^{6} + a^{5} b^{8} - a^{3} b^{10} - a b^{12}\right)} d^{3} \cos\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 12 \, {\left({\left(5 \, a^{7} + 4 \, a^{5} b^{2} - 9 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{6} b + 9 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(5 \, a^{5} b^{2} + 9 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - 4 \, {\left({\left(15 \, a^{7} + 19 \, a^{5} b^{2} - 4 \, a^{3} b^{4} - 8 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 2 \, b^{7} - {\left(25 \, a^{6} b + 49 \, a^{4} b^{3} + 26 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{12 \, {\left({\left(a^{6} b^{3} + a^{4} b^{5} - a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(12*sqrt(2)*((a^14*b^3 + 5*a^12*b^5 + 9*a^10*b^7 + 5*a^8*b^9 - 5*a^6*b^11 - 9*a^4*b^13 - 5*a^2*b^15 - b^17)*d^5*cos(d*x + c)^3 + 2*(a^13*b^4 + 6*a^11*b^6 + 15*a^9*b^8 + 20*a^7*b^10 + 15*a^5*b^12 + 6*a^3*b^14 + a*b^16)*d^5*cos(d*x + c)^2*sin(d*x + c) + (a^12*b^5 + 6*a^10*b^7 + 15*a^8*b^9 + 20*a^6*b^11 + 15*a^4*b^13 + 6*a^2*b^15 + b^17)*d^5*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 12*sqrt(2)*((a^14*b^3 + 5*a^12*b^5 + 9*a^10*b^7 + 5*a^8*b^9 - 5*a^6*b^11 - 9*a^4*b^13 - 5*a^2*b^15 - b^17)*d^5*cos(d*x + c)^3 + 2*(a^13*b^4 + 6*a^11*b^6 + 15*a^9*b^8 + 20*a^7*b^10 + 15*a^5*b^12 + 6*a^3*b^14 + a*b^16)*d^5*cos(d*x + c)^2*sin(d*x + c) + (a^12*b^5 + 6*a^10*b^7 + 15*a^8*b^9 + 20*a^6*b^11 + 15*a^4*b^13 + 6*a^2*b^15 + b^17)*d^5*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) - 3*sqrt(2)*((a^6*b^3 + a^4*b^5 - a^2*b^7 - b^9)*d*cos(d*x + c)^3 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^2*sin(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*d*cos(d*x + c) - 4*((a^9*b^4 - 2*a^5*b^8 + a*b^12)*d^3*cos(d*x + c)^3 + 2*(a^8*b^5 + a^6*b^7 - a^4*b^9 - a^2*b^11)*d^3*cos(d*x + c)^2*sin(d*x + c) + (a^7*b^6 + a^5*b^8 - a^3*b^10 - a*b^12)*d^3*cos(d*x + c))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^6*b^3 + a^4*b^5 - a^2*b^7 - b^9)*d*cos(d*x + c)^3 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^2*sin(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*d*cos(d*x + c) - 4*((a^9*b^4 - 2*a^5*b^8 + a*b^12)*d^3*cos(d*x + c)^3 + 2*(a^8*b^5 + a^6*b^7 - a^4*b^9 - a^2*b^11)*d^3*cos(d*x + c)^2*sin(d*x + c) + (a^7*b^6 + a^5*b^8 - a^3*b^10 - a*b^12)*d^3*cos(d*x + c))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + 3*((5*a^7 + 4*a^5*b^2 - 9*a^3*b^4)*cos(d*x + c)^3 + 2*(5*a^6*b + 9*a^4*b^3)*cos(d*x + c)^2*sin(d*x + c) + (5*a^5*b^2 + 9*a^3*b^4)*cos(d*x + c))*sqrt(-a/b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 4*((15*a^7 + 19*a^5*b^2 - 4*a^3*b^4 - 8*a*b^6)*cos(d*x + c)^3 + 8*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c) - (2*a^4*b^3 + 4*a^2*b^5 + 2*b^7 - (25*a^6*b + 49*a^4*b^3 + 26*a^2*b^5 + 2*b^7)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6*b^3 + a^4*b^5 - a^2*b^7 - b^9)*d*cos(d*x + c)^3 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^2*sin(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*d*cos(d*x + c)), 1/12*(12*sqrt(2)*((a^14*b^3 + 5*a^12*b^5 + 9*a^10*b^7 + 5*a^8*b^9 - 5*a^6*b^11 - 9*a^4*b^13 - 5*a^2*b^15 - b^17)*d^5*cos(d*x + c)^3 + 2*(a^13*b^4 + 6*a^11*b^6 + 15*a^9*b^8 + 20*a^7*b^10 + 15*a^5*b^12 + 6*a^3*b^14 + a*b^16)*d^5*cos(d*x + c)^2*sin(d*x + c) + (a^12*b^5 + 6*a^10*b^7 + 15*a^8*b^9 + 20*a^6*b^11 + 15*a^4*b^13 + 6*a^2*b^15 + b^17)*d^5*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 12*sqrt(2)*((a^14*b^3 + 5*a^12*b^5 + 9*a^10*b^7 + 5*a^8*b^9 - 5*a^6*b^11 - 9*a^4*b^13 - 5*a^2*b^15 - b^17)*d^5*cos(d*x + c)^3 + 2*(a^13*b^4 + 6*a^11*b^6 + 15*a^9*b^8 + 20*a^7*b^10 + 15*a^5*b^12 + 6*a^3*b^14 + a*b^16)*d^5*cos(d*x + c)^2*sin(d*x + c) + (a^12*b^5 + 6*a^10*b^7 + 15*a^8*b^9 + 20*a^6*b^11 + 15*a^4*b^13 + 6*a^2*b^15 + b^17)*d^5*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) - 3*sqrt(2)*((a^6*b^3 + a^4*b^5 - a^2*b^7 - b^9)*d*cos(d*x + c)^3 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^2*sin(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*d*cos(d*x + c) - 4*((a^9*b^4 - 2*a^5*b^8 + a*b^12)*d^3*cos(d*x + c)^3 + 2*(a^8*b^5 + a^6*b^7 - a^4*b^9 - a^2*b^11)*d^3*cos(d*x + c)^2*sin(d*x + c) + (a^7*b^6 + a^5*b^8 - a^3*b^10 - a*b^12)*d^3*cos(d*x + c))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + 3*sqrt(2)*((a^6*b^3 + a^4*b^5 - a^2*b^7 - b^9)*d*cos(d*x + c)^3 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^2*sin(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*d*cos(d*x + c) - 4*((a^9*b^4 - 2*a^5*b^8 + a*b^12)*d^3*cos(d*x + c)^3 + 2*(a^8*b^5 + a^6*b^7 - a^4*b^9 - a^2*b^11)*d^3*cos(d*x + c)^2*sin(d*x + c) + (a^7*b^6 + a^5*b^8 - a^3*b^10 - a*b^12)*d^3*cos(d*x + c))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + 12*((5*a^7 + 4*a^5*b^2 - 9*a^3*b^4)*cos(d*x + c)^3 + 2*(5*a^6*b + 9*a^4*b^3)*cos(d*x + c)^2*sin(d*x + c) + (5*a^5*b^2 + 9*a^3*b^4)*cos(d*x + c))*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) - 4*((15*a^7 + 19*a^5*b^2 - 4*a^3*b^4 - 8*a*b^6)*cos(d*x + c)^3 + 8*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*cos(d*x + c) - (2*a^4*b^3 + 4*a^2*b^5 + 2*b^7 - (25*a^6*b + 49*a^4*b^3 + 26*a^2*b^5 + 2*b^7)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6*b^3 + a^4*b^5 - a^2*b^7 - b^9)*d*cos(d*x + c)^3 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^2*sin(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*d*cos(d*x + c))]","B",0
592,1,14311,0,12.840384," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(a^{14} b^{2} + 5 \, a^{12} b^{4} + 9 \, a^{10} b^{6} + 5 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 9 \, a^{4} b^{12} - 5 \, a^{2} b^{14} - b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{3} + 6 \, a^{11} b^{5} + 15 \, a^{9} b^{7} + 20 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 6 \, a^{3} b^{13} + a b^{15}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{4} + 6 \, a^{10} b^{6} + 15 \, a^{8} b^{8} + 20 \, a^{6} b^{10} + 15 \, a^{4} b^{12} + 6 \, a^{2} b^{14} + b^{16}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} b^{2} + 5 \, a^{12} b^{4} + 9 \, a^{10} b^{6} + 5 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 9 \, a^{4} b^{12} - 5 \, a^{2} b^{14} - b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{3} + 6 \, a^{11} b^{5} + 15 \, a^{9} b^{7} + 20 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 6 \, a^{3} b^{13} + a b^{15}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{4} + 6 \, a^{10} b^{6} + 15 \, a^{8} b^{8} + 20 \, a^{6} b^{10} + 15 \, a^{4} b^{12} + 6 \, a^{2} b^{14} + b^{16}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + \sqrt{2} {\left({\left(a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{9} b^{3} - 2 \, a^{5} b^{7} + a b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{4} + a^{6} b^{6} - a^{4} b^{8} - a^{2} b^{10}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{9} b^{3} - 2 \, a^{5} b^{7} + a b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{4} + a^{6} b^{6} - a^{4} b^{8} - a^{2} b^{10}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + {\left(3 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{3} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 4 \, {\left(2 \, a^{4} b^{2} + 4 \, a^{2} b^{4} + 2 \, b^{6} + {\left(3 \, a^{6} + 3 \, a^{4} b^{2} - 2 \, a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{5} b + 9 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left({\left(a^{14} b^{2} + 5 \, a^{12} b^{4} + 9 \, a^{10} b^{6} + 5 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 9 \, a^{4} b^{12} - 5 \, a^{2} b^{14} - b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{3} + 6 \, a^{11} b^{5} + 15 \, a^{9} b^{7} + 20 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 6 \, a^{3} b^{13} + a b^{15}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{4} + 6 \, a^{10} b^{6} + 15 \, a^{8} b^{8} + 20 \, a^{6} b^{10} + 15 \, a^{4} b^{12} + 6 \, a^{2} b^{14} + b^{16}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} b^{2} + 5 \, a^{12} b^{4} + 9 \, a^{10} b^{6} + 5 \, a^{8} b^{8} - 5 \, a^{6} b^{10} - 9 \, a^{4} b^{12} - 5 \, a^{2} b^{14} - b^{16}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{3} + 6 \, a^{11} b^{5} + 15 \, a^{9} b^{7} + 20 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 6 \, a^{3} b^{13} + a b^{15}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{4} + 6 \, a^{10} b^{6} + 15 \, a^{8} b^{8} + 20 \, a^{6} b^{10} + 15 \, a^{4} b^{12} + 6 \, a^{2} b^{14} + b^{16}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + \sqrt{2} {\left({\left(a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{9} b^{3} - 2 \, a^{5} b^{7} + a b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{4} + a^{6} b^{6} - a^{4} b^{8} - a^{2} b^{10}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d + 4 \, {\left({\left(a^{9} b^{3} - 2 \, a^{5} b^{7} + a b^{11}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{4} + a^{6} b^{6} - a^{4} b^{8} - a^{2} b^{10}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{5} + a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, {\left(3 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - 7 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{3} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) + 4 \, {\left(2 \, a^{4} b^{2} + 4 \, a^{2} b^{4} + 2 \, b^{6} + {\left(3 \, a^{6} + 3 \, a^{4} b^{2} - 2 \, a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{5} b + 9 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*((a^14*b^2 + 5*a^12*b^4 + 9*a^10*b^6 + 5*a^8*b^8 - 5*a^6*b^10 - 9*a^4*b^12 - 5*a^2*b^14 - b^16)*d^5*cos(d*x + c)^2 + 2*(a^13*b^3 + 6*a^11*b^5 + 15*a^9*b^7 + 20*a^7*b^9 + 15*a^5*b^11 + 6*a^3*b^13 + a*b^15)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^4 + 6*a^10*b^6 + 15*a^8*b^8 + 20*a^6*b^10 + 15*a^4*b^12 + 6*a^2*b^14 + b^16)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14*b^2 + 5*a^12*b^4 + 9*a^10*b^6 + 5*a^8*b^8 - 5*a^6*b^10 - 9*a^4*b^12 - 5*a^2*b^14 - b^16)*d^5*cos(d*x + c)^2 + 2*(a^13*b^3 + 6*a^11*b^5 + 15*a^9*b^7 + 20*a^7*b^9 + 15*a^5*b^11 + 6*a^3*b^13 + a*b^15)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^4 + 6*a^10*b^6 + 15*a^8*b^8 + 20*a^6*b^10 + 15*a^4*b^12 + 6*a^2*b^14 + b^16)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + sqrt(2)*((a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^9*b^3 - 2*a^5*b^7 + a*b^11)*d^3*cos(d*x + c)^2 + 2*(a^8*b^4 + a^6*b^6 - a^4*b^8 - a^2*b^10)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^9*b^3 - 2*a^5*b^7 + a*b^11)*d^3*cos(d*x + c)^2 + 2*(a^8*b^4 + a^6*b^6 - a^4*b^8 - a^2*b^10)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + (3*a^4*b^2 + 7*a^2*b^4 + (3*a^6 + 4*a^4*b^2 - 7*a^2*b^4)*cos(d*x + c)^2 + 2*(3*a^5*b + 7*a^3*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 4*(2*a^4*b^2 + 4*a^2*b^4 + 2*b^6 + (3*a^6 + 3*a^4*b^2 - 2*a^2*b^4 - 2*b^6)*cos(d*x + c)^2 + (5*a^5*b + 9*a^3*b^3 + 4*a*b^5)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*d), 1/4*(4*sqrt(2)*((a^14*b^2 + 5*a^12*b^4 + 9*a^10*b^6 + 5*a^8*b^8 - 5*a^6*b^10 - 9*a^4*b^12 - 5*a^2*b^14 - b^16)*d^5*cos(d*x + c)^2 + 2*(a^13*b^3 + 6*a^11*b^5 + 15*a^9*b^7 + 20*a^7*b^9 + 15*a^5*b^11 + 6*a^3*b^13 + a*b^15)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^4 + 6*a^10*b^6 + 15*a^8*b^8 + 20*a^6*b^10 + 15*a^4*b^12 + 6*a^2*b^14 + b^16)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14*b^2 + 5*a^12*b^4 + 9*a^10*b^6 + 5*a^8*b^8 - 5*a^6*b^10 - 9*a^4*b^12 - 5*a^2*b^14 - b^16)*d^5*cos(d*x + c)^2 + 2*(a^13*b^3 + 6*a^11*b^5 + 15*a^9*b^7 + 20*a^7*b^9 + 15*a^5*b^11 + 6*a^3*b^13 + a*b^15)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^4 + 6*a^10*b^6 + 15*a^8*b^8 + 20*a^6*b^10 + 15*a^4*b^12 + 6*a^2*b^14 + b^16)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + sqrt(2)*((a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^9*b^3 - 2*a^5*b^7 + a*b^11)*d^3*cos(d*x + c)^2 + 2*(a^8*b^4 + a^6*b^6 - a^4*b^8 - a^2*b^10)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*d + 4*((a^9*b^3 - 2*a^5*b^7 + a*b^11)*d^3*cos(d*x + c)^2 + 2*(a^8*b^4 + a^6*b^6 - a^4*b^8 - a^2*b^10)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^5 + a^5*b^7 - a^3*b^9 - a*b^11)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - 4*(3*a^4*b^2 + 7*a^2*b^4 + (3*a^6 + 4*a^4*b^2 - 7*a^2*b^4)*cos(d*x + c)^2 + 2*(3*a^5*b + 7*a^3*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) + 4*(2*a^4*b^2 + 4*a^2*b^4 + 2*b^6 + (3*a^6 + 3*a^4*b^2 - 2*a^2*b^4 - 2*b^6)*cos(d*x + c)^2 + (5*a^5*b + 9*a^3*b^3 + 4*a*b^5)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*d)]","B",0
593,1,14258,0,11.626478," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left({\left(a^{14} b + 5 \, a^{12} b^{3} + 9 \, a^{10} b^{5} + 5 \, a^{8} b^{7} - 5 \, a^{6} b^{9} - 9 \, a^{4} b^{11} - 5 \, a^{2} b^{13} - b^{15}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} b + 5 \, a^{12} b^{3} + 9 \, a^{10} b^{5} + 5 \, a^{8} b^{7} - 5 \, a^{6} b^{9} - 9 \, a^{4} b^{11} - 5 \, a^{2} b^{13} - b^{15}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) - \sqrt{2} {\left({\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d - 4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{5} b^{6} + a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d - 4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{5} b^{6} + a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - {\left(a^{3} b^{2} + 5 \, a b^{4} + {\left(a^{5} + 4 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 5 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d\right)}}, -\frac{4 \, \sqrt{2} {\left({\left(a^{14} b + 5 \, a^{12} b^{3} + 9 \, a^{10} b^{5} + 5 \, a^{8} b^{7} - 5 \, a^{6} b^{9} - 9 \, a^{4} b^{11} - 5 \, a^{2} b^{13} - b^{15}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} b + 5 \, a^{12} b^{3} + 9 \, a^{10} b^{5} + 5 \, a^{8} b^{7} - 5 \, a^{6} b^{9} - 9 \, a^{4} b^{11} - 5 \, a^{2} b^{13} - b^{15}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{3} + 6 \, a^{10} b^{5} + 15 \, a^{8} b^{7} + 20 \, a^{6} b^{9} + 15 \, a^{4} b^{11} + 6 \, a^{2} b^{13} + b^{15}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) - \sqrt{2} {\left({\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d - 4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{5} b^{6} + a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d - 4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{5} b^{6} + a b^{10}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{4} + a^{5} b^{6} - a^{3} b^{8} - a b^{10}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, {\left(a^{3} b^{2} + 5 \, a b^{4} + {\left(a^{5} + 4 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 5 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d\right)}}\right]"," ",0,"[-1/4*(4*sqrt(2)*((a^14*b + 5*a^12*b^3 + 9*a^10*b^5 + 5*a^8*b^7 - 5*a^6*b^9 - 9*a^4*b^11 - 5*a^2*b^13 - b^15)*d^5*cos(d*x + c)^2 + 2*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14*b + 5*a^12*b^3 + 9*a^10*b^5 + 5*a^8*b^7 - 5*a^6*b^9 - 9*a^4*b^11 - 5*a^2*b^13 - b^15)*d^5*cos(d*x + c)^2 + 2*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) - sqrt(2)*((a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d*cos(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d - 4*((a^9*b^2 - 2*a^5*b^6 + a*b^10)*d^3*cos(d*x + c)^2 + 2*(a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*((a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d*cos(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d - 4*((a^9*b^2 - 2*a^5*b^6 + a*b^10)*d^3*cos(d*x + c)^2 + 2*(a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - (a^3*b^2 + 5*a*b^4 + (a^5 + 4*a^3*b^2 - 5*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b + 5*a^2*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 4*((a^5 + a^3*b^2)*cos(d*x + c)^2 + (a^4*b + a^2*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d*cos(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d), -1/4*(4*sqrt(2)*((a^14*b + 5*a^12*b^3 + 9*a^10*b^5 + 5*a^8*b^7 - 5*a^6*b^9 - 9*a^4*b^11 - 5*a^2*b^13 - b^15)*d^5*cos(d*x + c)^2 + 2*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14*b + 5*a^12*b^3 + 9*a^10*b^5 + 5*a^8*b^7 - 5*a^6*b^9 - 9*a^4*b^11 - 5*a^2*b^13 - b^15)*d^5*cos(d*x + c)^2 + 2*(a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^3 + 6*a^10*b^5 + 15*a^8*b^7 + 20*a^6*b^9 + 15*a^4*b^11 + 6*a^2*b^13 + b^15)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) - sqrt(2)*((a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d*cos(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d - 4*((a^9*b^2 - 2*a^5*b^6 + a*b^10)*d^3*cos(d*x + c)^2 + 2*(a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*((a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d*cos(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d - 4*((a^9*b^2 - 2*a^5*b^6 + a*b^10)*d^3*cos(d*x + c)^2 + 2*(a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^4 + a^5*b^6 - a^3*b^8 - a*b^10)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - 4*(a^3*b^2 + 5*a*b^4 + (a^5 + 4*a^3*b^2 - 5*a*b^4)*cos(d*x + c)^2 + 2*(a^4*b + 5*a^2*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) + 4*((a^5 + a^3*b^2)*cos(d*x + c)^2 + (a^4*b + a^2*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d*cos(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d)]","B",0
594,1,14125,0,12.230106," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d + 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d + 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + {\left(a^{2} b^{2} - 3 \, b^{4} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} - 4 \, {\left(a b \cos\left(d x + c\right)^{2} - b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}, -\frac{4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d + 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d + 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, {\left(a^{2} b^{2} - 3 \, b^{4} + {\left(a^{4} - 4 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{a}\right) - 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*(4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d + 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d + 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + (a^2*b^2 - 3*b^4 + (a^4 - 4*a^2*b^2 + 3*b^4)*cos(d*x + c)^2 + 2*(a^3*b - 3*a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 - 4*(a*b*cos(d*x + c)^2 - b^2*cos(d*x + c)*sin(d*x + c))*sqrt(-a/b)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 4*((a^4 + a^2*b^2)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d), -1/4*(4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d + 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d + 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - 4*(a^2*b^2 - 3*b^4 + (a^4 - 4*a^2*b^2 + 3*b^4)*cos(d*x + c)^2 + 2*(a^3*b - 3*a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(a/b)*arctan(b*sqrt(a/b)*sqrt(sin(d*x + c)/cos(d*x + c))/a) - 4*((a^4 + a^2*b^2)*cos(d*x + c)^2 + (a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)]","B",0
595,1,14310,0,12.648296," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) - \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d - 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d - 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - {\left(3 \, a^{2} b^{2} - b^{4} + {\left(3 \, a^{4} - 4 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{12} b^{2} + 6 \, a^{10} b^{4} + 15 \, a^{8} b^{6} + 20 \, a^{6} b^{8} + 15 \, a^{4} b^{10} + 6 \, a^{2} b^{12} + b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left(2 \, {\left(a^{17} b + 8 \, a^{15} b^{3} + 28 \, a^{13} b^{5} + 56 \, a^{11} b^{7} + 70 \, a^{9} b^{9} + 56 \, a^{7} b^{11} + 28 \, a^{5} b^{13} + 8 \, a^{3} b^{15} + a b^{17}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{14} + 5 \, a^{12} b^{2} + 9 \, a^{10} b^{4} + 5 \, a^{8} b^{6} - 5 \, a^{6} b^{8} - 9 \, a^{4} b^{10} - 5 \, a^{2} b^{12} - b^{14}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(2 \, {\left(a^{21} b + 2 \, a^{19} b^{3} - 19 \, a^{17} b^{5} - 104 \, a^{15} b^{7} - 238 \, a^{13} b^{9} - 308 \, a^{11} b^{11} - 238 \, a^{9} b^{13} - 104 \, a^{7} b^{15} - 19 \, a^{5} b^{17} + 2 \, a^{3} b^{19} + a b^{21}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - {\left(a^{18} - a^{16} b^{2} - 20 \, a^{14} b^{4} - 44 \, a^{12} b^{6} - 26 \, a^{10} b^{8} + 26 \, a^{8} b^{10} + 44 \, a^{6} b^{12} + 20 \, a^{4} b^{14} + a^{2} b^{16} - b^{18}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) - \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d - 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d - 4 \, {\left({\left(a^{9} b - 2 \, a^{5} b^{5} + a b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{3} + a^{5} b^{5} - a^{3} b^{7} - a b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left({\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - 2 \, {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 4 \, {\left(3 \, a^{2} b^{2} - b^{4} + {\left(3 \, a^{4} - 4 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(2 \, a^{2} b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right) - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) - sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d - 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d - 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - (3*a^2*b^2 - b^4 + (3*a^4 - 4*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*(3*a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a^2*cos(d*x + c)^2 - a*b*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 4*((a^3*b + a*b^3)*cos(d*x + c)^2 + (a^2*b^2 + b^4)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d), 1/4*(4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*cos(d*x + c)^2 + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^12*b^2 + 6*a^10*b^4 + 15*a^8*b^6 + 20*a^6*b^8 + 15*a^4*b^10 + 6*a^2*b^12 + b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*(2*(a^17*b + 8*a^15*b^3 + 28*a^13*b^5 + 56*a^11*b^7 + 70*a^9*b^9 + 56*a^7*b^11 + 28*a^5*b^13 + 8*a^3*b^15 + a*b^17)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^14 + 5*a^12*b^2 + 9*a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - 9*a^4*b^10 - 5*a^2*b^12 - b^14)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*(2*(a^21*b + 2*a^19*b^3 - 19*a^17*b^5 - 104*a^15*b^7 - 238*a^13*b^9 - 308*a^11*b^11 - 238*a^9*b^13 - 104*a^7*b^15 - 19*a^5*b^17 + 2*a^3*b^19 + a*b^21)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - (a^18 - a^16*b^2 - 20*a^14*b^4 - 44*a^12*b^6 - 26*a^10*b^8 + 26*a^8*b^10 + 44*a^6*b^12 + 20*a^4*b^14 + a^2*b^16 - b^18)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) - sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d - 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + sqrt(2)*((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d - 4*((a^9*b - 2*a^5*b^5 + a*b^9)*d^3*cos(d*x + c)^2 + 2*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^7*b^3 + a^5*b^5 - a^3*b^7 - a*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*((a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - 2*(a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - 4*(3*a^2*b^2 - b^4 + (3*a^4 - 4*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*(3*a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(b/a)*arctan((2*a^2*b*cos(d*x + c)^2*sin(d*x + c) + a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sqrt(b/a)*sqrt(sin(d*x + c)/cos(d*x + c))/(2*a*b^2*cos(d*x + c)^3 - 2*a*b^2*cos(d*x + c) - (b^3 + (a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))) - 4*((a^3*b + a*b^3)*cos(d*x + c)^2 + (a^2*b^2 + b^4)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)]","B",0
596,1,14311,0,12.303056," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left({\left(a^{15} + 5 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 5 \, a^{9} b^{6} - 5 \, a^{7} b^{8} - 9 \, a^{5} b^{10} - 5 \, a^{3} b^{12} - a b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{15} + 5 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 5 \, a^{9} b^{6} - 5 \, a^{7} b^{8} - 9 \, a^{5} b^{10} - 5 \, a^{3} b^{12} - a b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + \sqrt{2} {\left({\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d + 4 \, {\left({\left(a^{10} b - 2 \, a^{6} b^{5} + a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{2} + a^{7} b^{4} - a^{5} b^{6} - a^{3} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d + 4 \, {\left({\left(a^{10} b - 2 \, a^{6} b^{5} + a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{2} + a^{7} b^{4} - a^{5} b^{6} - a^{3} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + {\left(5 \, a^{2} b^{3} + b^{5} + {\left(5 \, a^{4} b - 4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(-\frac{6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - b^{2} + 4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 4 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}, \frac{4 \, \sqrt{2} {\left({\left(a^{15} + 5 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 5 \, a^{9} b^{6} - 5 \, a^{7} b^{8} - 9 \, a^{5} b^{10} - 5 \, a^{3} b^{12} - a b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} - \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + 4 \, \sqrt{2} {\left({\left(a^{15} + 5 \, a^{13} b^{2} + 9 \, a^{11} b^{4} + 5 \, a^{9} b^{6} - 5 \, a^{7} b^{8} - 9 \, a^{5} b^{10} - 5 \, a^{3} b^{12} - a b^{14}\right)} d^{5} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{14} b + 6 \, a^{12} b^{3} + 15 \, a^{10} b^{5} + 20 \, a^{8} b^{7} + 15 \, a^{6} b^{9} + 6 \, a^{4} b^{11} + a^{2} b^{13}\right)} d^{5} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{13} b^{2} + 6 \, a^{11} b^{4} + 15 \, a^{9} b^{6} + 20 \, a^{7} b^{8} + 15 \, a^{5} b^{10} + 6 \, a^{3} b^{12} + a b^{14}\right)} d^{5}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{4} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + \sqrt{2} {\left({\left(a^{18} + 7 \, a^{16} b^{2} + 20 \, a^{14} b^{4} + 28 \, a^{12} b^{6} + 14 \, a^{10} b^{8} - 14 \, a^{8} b^{10} - 28 \, a^{6} b^{12} - 20 \, a^{4} b^{14} - 7 \, a^{2} b^{16} - b^{18}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{13} b + 6 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 20 \, a^{7} b^{7} + 15 \, a^{5} b^{9} + 6 \, a^{3} b^{11} + a b^{13}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(a^{22} + a^{20} b^{2} - 21 \, a^{18} b^{4} - 85 \, a^{16} b^{6} - 134 \, a^{14} b^{8} - 70 \, a^{12} b^{10} + 70 \, a^{10} b^{12} + 134 \, a^{8} b^{14} + 85 \, a^{6} b^{16} + 21 \, a^{4} b^{18} - a^{2} b^{20} - b^{22}\right)} d^{7} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} + 2 \, {\left(a^{17} b - 20 \, a^{13} b^{5} - 64 \, a^{11} b^{7} - 90 \, a^{9} b^{9} - 64 \, a^{7} b^{11} - 20 \, a^{5} b^{13} + a b^{17}\right)} d^{5} \sqrt{\frac{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}{{\left(a^{16} + 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} + 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} + 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} + 8 \, a^{2} b^{14} + b^{16}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{3}{4}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}\right) + \sqrt{2} {\left({\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d + 4 \, {\left({\left(a^{10} b - 2 \, a^{6} b^{5} + a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{2} + a^{7} b^{4} - a^{5} b^{6} - a^{3} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \sqrt{2} {\left({\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d + 4 \, {\left({\left(a^{10} b - 2 \, a^{6} b^{5} + a^{2} b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b^{2} + a^{7} b^{4} - a^{5} b^{6} - a^{3} b^{8}\right)} d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{3} + a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9}\right)} d^{3}\right)} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} {\left(2 \, {\left(a^{13} b - 10 \, a^{11} b^{3} + 15 \, a^{9} b^{5} + 52 \, a^{7} b^{7} + 15 \, a^{5} b^{9} - 10 \, a^{3} b^{11} + a b^{13}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}} \cos\left(d x + c\right) + {\left(a^{10} - 13 \, a^{8} b^{2} + 50 \, a^{6} b^{4} - 50 \, a^{4} b^{6} + 13 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}}}{a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{4}}\right)^{\frac{1}{4}} + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 4 \, {\left(5 \, a^{2} b^{3} + b^{5} + {\left(5 \, a^{4} b - 4 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(2 \, a^{2} b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{\frac{b}{a}} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{2 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(b^{3} + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}\right) + 4 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, {\left({\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*((a^15 + 5*a^13*b^2 + 9*a^11*b^4 + 5*a^9*b^6 - 5*a^7*b^8 - 9*a^5*b^10 - 5*a^3*b^12 - a*b^14)*d^5*cos(d*x + c)^2 + 2*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^15 + 5*a^13*b^2 + 9*a^11*b^4 + 5*a^9*b^6 - 5*a^7*b^8 - 9*a^5*b^10 - 5*a^3*b^12 - a*b^14)*d^5*cos(d*x + c)^2 + 2*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + sqrt(2)*((a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d*cos(d*x + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d + 4*((a^10*b - 2*a^6*b^5 + a^2*b^9)*d^3*cos(d*x + c)^2 + 2*(a^9*b^2 + a^7*b^4 - a^5*b^6 - a^3*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d*cos(d*x + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d + 4*((a^10*b - 2*a^6*b^5 + a^2*b^9)*d^3*cos(d*x + c)^2 + 2*(a^9*b^2 + a^7*b^4 - a^5*b^6 - a^3*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + (5*a^2*b^3 + b^5 + (5*a^4*b - 4*a^2*b^3 - b^5)*cos(d*x + c)^2 + 2*(5*a^3*b^2 + a*b^4)*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*log(-(6*a*b*cos(d*x + c)*sin(d*x + c) - (a^2 - b^2)*cos(d*x + c)^2 - b^2 + 4*(a^2*cos(d*x + c)^2 - a*b*cos(d*x + c)*sin(d*x + c))*sqrt(-b/a)*sqrt(sin(d*x + c)/cos(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 4*((a^3*b^2 + a*b^4)*cos(d*x + c)^2 + (a^2*b^3 + b^5)*cos(d*x + c)*sin(d*x + c))*sqrt(sin(d*x + c)/cos(d*x + c)))/((a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d*cos(d*x + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d), 1/4*(4*sqrt(2)*((a^15 + 5*a^13*b^2 + 9*a^11*b^4 + 5*a^9*b^6 - 5*a^7*b^8 - 9*a^5*b^10 - 5*a^3*b^12 - a*b^14)*d^5*cos(d*x + c)^2 + 2*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) - sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) + sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + 4*sqrt(2)*((a^15 + 5*a^13*b^2 + 9*a^11*b^4 + 5*a^9*b^6 - 5*a^7*b^8 - 9*a^5*b^10 - 5*a^3*b^12 - a*b^14)*d^5*cos(d*x + c)^2 + 2*(a^14*b + 6*a^12*b^3 + 15*a^10*b^5 + 20*a^8*b^7 + 15*a^6*b^9 + 6*a^4*b^11 + a^2*b^13)*d^5*cos(d*x + c)*sin(d*x + c) + (a^13*b^2 + 6*a^11*b^4 + 15*a^9*b^6 + 20*a^7*b^8 + 15*a^5*b^10 + 6*a^3*b^12 + a*b^14)*d^5)*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4)*arctan(-((a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^4*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + sqrt(2)*((a^18 + 7*a^16*b^2 + 20*a^14*b^4 + 28*a^12*b^6 + 14*a^10*b^8 - 14*a^8*b^10 - 28*a^6*b^12 - 20*a^4*b^14 - 7*a^2*b^16 - b^18)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^13*b + 6*a^11*b^3 + 15*a^9*b^5 + 20*a^7*b^7 + 15*a^5*b^9 + 6*a^3*b^11 + a*b^13)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4) - sqrt(2)*((a^22 + a^20*b^2 - 21*a^18*b^4 - 85*a^16*b^6 - 134*a^14*b^8 - 70*a^12*b^10 + 70*a^10*b^12 + 134*a^8*b^14 + 85*a^6*b^16 + 21*a^4*b^18 - a^2*b^20 - b^22)*d^7*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4))*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)) + 2*(a^17*b - 20*a^13*b^5 - 64*a^11*b^7 - 90*a^9*b^9 - 64*a^7*b^11 - 20*a^5*b^13 + a*b^17)*d^5*sqrt((a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)/((a^16 + 8*a^14*b^2 + 28*a^12*b^4 + 56*a^10*b^6 + 70*a^8*b^8 + 56*a^6*b^10 + 28*a^4*b^12 + 8*a^2*b^14 + b^16)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(3/4))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)) + sqrt(2)*((a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d*cos(d*x + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d + 4*((a^10*b - 2*a^6*b^5 + a^2*b^9)*d^3*cos(d*x + c)^2 + 2*(a^9*b^2 + a^7*b^4 - a^5*b^6 - a^3*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) - sqrt(2)*((a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d*cos(d*x + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d + 4*((a^10*b - 2*a^6*b^5 + a^2*b^9)*d^3*cos(d*x + c)^2 + 2*(a^9*b^2 + a^7*b^4 - a^5*b^6 - a^3*b^8)*d^3*cos(d*x + c)*sin(d*x + c) + (a^8*b^3 + a^6*b^5 - a^4*b^7 - a^2*b^9)*d^3)*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4)*log(((a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) - sqrt(2)*(2*(a^13*b - 10*a^11*b^3 + 15*a^9*b^5 + 52*a^7*b^7 + 15*a^5*b^9 - 10*a^3*b^11 + a*b^13)*d^3*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))*cos(d*x + c) + (a^10 - 13*a^8*b^2 + 50*a^6*b^4 - 50*a^4*b^6 + 13*a^2*b^8 - b^10)*d*cos(d*x + c))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8 - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*d^2*sqrt(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4)))/(a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8))*sqrt(sin(d*x + c)/cos(d*x + c))*(1/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^4))^(1/4) + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*sin(d*x + c))/cos(d*x + c)) + 4*(5*a^2*b^3 + b^5 + (5*a^4*b - 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681,1,3557,0,1.122703," ","integrate(tan(f*x+e)^4*(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{70 \, d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) \log\left(2 \, c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 280 \, d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \arctan\left(-\frac{c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - \sqrt{2 \, c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + {\left(c^{4} + c^{2} d^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)}{{\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)}\right) \cos\left(f x + e\right)^{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 140 \, {\left(\sqrt{3} d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \arctan\left(-\frac{2 \, c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - 2 \, {\left(\sqrt{3} c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 2 \, {\left(\sqrt{3} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sqrt{\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} + \sqrt{3} {\left(c^{4} + c^{2} d^{2}\right)}}{3 \, c^{4} + 3 \, c^{2} d^{2} - 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)^{2}}\right) + 140 \, {\left(\sqrt{3} d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \arctan\left(\frac{2 \, c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 2 \, {\left(\sqrt{3} c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sqrt{-\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} - \sqrt{3} {\left(c^{4} + c^{2} d^{2}\right)}}{3 \, c^{4} + 3 \, c^{2} d^{2} - 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)^{2}}\right) - 35 \, {\left(\sqrt{3} d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \log\left(\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 35 \, {\left(\sqrt{3} d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - d^{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \log\left(-\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 3 \, {\left(2 \, c d^{2} \cos\left(f x + e\right) + {\left(9 \, c^{3} - 37 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(14 \, d^{3} - {\left(3 \, c^{2} d + 49 \, d^{3}\right)} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}}}{140 \, d^{3} f \cos\left(f x + e\right)^{3}}"," ",0,"1/140*(70*d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))*log(2*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 280*d^3*f*((c^2 + d^2)/f^6)^(1/6)*arctan(-(c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) - sqrt(2*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3))*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) + (c^4 + c^2*d^2)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))/((c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))))*cos(f*x + e)^3*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + 140*(sqrt(3)*d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*arctan(-(2*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - 2*(sqrt(3)*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) + 2*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + 2*(sqrt(3)*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sqrt(sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + sqrt(3)*(c^4 + c^2*d^2))/(3*c^4 + 3*c^2*d^2 - 4*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))^2)) + 140*(sqrt(3)*d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*arctan((2*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + 2*(sqrt(3)*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) - 2*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - 2*(sqrt(3)*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sqrt(-sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - sqrt(3)*(c^4 + c^2*d^2))/(3*c^4 + 3*c^2*d^2 - 4*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))^2)) - 35*(sqrt(3)*d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*log(sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 35*(sqrt(3)*d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - d^3*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^3*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*log(-sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 3*(2*c*d^2*cos(f*x + e) + (9*c^3 - 37*c*d^2)*cos(f*x + e)^3 + (14*d^3 - (3*c^2*d + 49*d^3)*cos(f*x + e)^2)*sin(f*x + e))*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3))/(d^3*f*cos(f*x + e)^3)","B",0
682,1,2930,0,2.012681," ","integrate(tan(f*x+e)^3*(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{14 \, d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) \log\left(2 \, f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) - 56 \, d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \arctan\left(\frac{\sqrt{2 \, f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)}{{\left(c^{2} + d^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)}\right) \cos\left(f x + e\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 28 \, {\left(\sqrt{3} d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \arctan\left(-\frac{2 \, \sqrt{3} f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + 2 \, {\left(f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - 2 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sqrt{-\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} - \sqrt{3} {\left(c^{2} + d^{2}\right)}}{4 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)^{2} - c^{2} - d^{2}}\right) + 28 \, {\left(\sqrt{3} d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \arctan\left(\frac{2 \, \sqrt{3} f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 2 \, {\left(f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - 2 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sqrt{\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} - \sqrt{3} {\left(c^{2} + d^{2}\right)}}{4 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)^{2} - c^{2} - d^{2}}\right) + 7 \, {\left(\sqrt{3} d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \log\left(\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) - 7 \, {\left(\sqrt{3} d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + d^{2} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right)^{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \log\left(-\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 3 \, {\left(c d \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(3 \, c^{2} + 32 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 4 \, d^{2}\right)} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}}}{28 \, d^{2} f \cos\left(f x + e\right)^{2}}"," ",0,"1/28*(14*d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2))*log(2*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - 56*d^2*f*((c^2 + d^2)/f^6)^(1/6)*arctan((sqrt(2*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3))*f^5*((c^2 + d^2)/f^6)^(5/6) - f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6) - (c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))/((c^2 + d^2)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2))))*cos(f*x + e)^2*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - 28*(sqrt(3)*d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*arctan(-(2*sqrt(3)*f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + 2*(f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6) - 2*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - 2*(sqrt(3)*f^5*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^5*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*sqrt(-sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - sqrt(3)*(c^2 + d^2))/(4*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2))^2 - c^2 - d^2)) + 28*(sqrt(3)*d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*arctan((2*sqrt(3)*f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - 2*(f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6) - 2*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - 2*(sqrt(3)*f^5*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - f^5*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*sqrt(sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - sqrt(3)*(c^2 + d^2))/(4*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2))^2 - c^2 - d^2)) + 7*(sqrt(3)*d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*log(sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - 7*(sqrt(3)*d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + d^2*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)^2*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)))*log(-sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) - f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) + c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 3*(c*d*cos(f*x + e)*sin(f*x + e) - (3*c^2 + 32*d^2)*cos(f*x + e)^2 + 4*d^2)*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3))/(d^2*f*cos(f*x + e)^2)","B",0
683,1,3498,0,1.261582," ","integrate(tan(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{2 \, d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) \log\left(2 \, c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 8 \, d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \arctan\left(-\frac{c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - \sqrt{2 \, c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + {\left(c^{4} + c^{2} d^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)}{{\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)}\right) \cos\left(f x + e\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 4 \, {\left(\sqrt{3} d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \arctan\left(-\frac{2 \, c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - 2 \, {\left(\sqrt{3} c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 2 \, {\left(\sqrt{3} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sqrt{\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} + \sqrt{3} {\left(c^{4} + c^{2} d^{2}\right)}}{3 \, c^{4} + 3 \, c^{2} d^{2} - 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)^{2}}\right) + 4 \, {\left(\sqrt{3} d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \arctan\left(\frac{2 \, c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 2 \, {\left(\sqrt{3} c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sqrt{-\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} - \sqrt{3} {\left(c^{4} + c^{2} d^{2}\right)}}{3 \, c^{4} + 3 \, c^{2} d^{2} - 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)^{2}}\right) - {\left(\sqrt{3} d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \log\left(\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + {\left(\sqrt{3} d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - d f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(f x + e\right) \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \log\left(-\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 3 \, {\left(c \cos\left(f x + e\right) + d \sin\left(f x + e\right)\right)} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}}}{4 \, d f \cos\left(f x + e\right)}"," ",0,"1/4*(2*d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2))*log(2*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 8*d*f*((c^2 + d^2)/f^6)^(1/6)*arctan(-(c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) - sqrt(2*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3))*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) + (c^4 + c^2*d^2)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))/((c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2))))*cos(f*x + e)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + 4*(sqrt(3)*d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*arctan(-(2*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - 2*(sqrt(3)*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) + 2*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + 2*(sqrt(3)*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*sqrt(sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + sqrt(3)*(c^4 + c^2*d^2))/(3*c^4 + 3*c^2*d^2 - 4*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2))^2)) + 4*(sqrt(3)*d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*arctan((2*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + 2*(sqrt(3)*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) - 2*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - 2*(sqrt(3)*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*sqrt(-sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - sqrt(3)*(c^4 + c^2*d^2))/(3*c^4 + 3*c^2*d^2 - 4*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2))^2)) - (sqrt(3)*d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*log(sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + (sqrt(3)*d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - d*f*((c^2 + d^2)/f^6)^(1/6)*cos(f*x + e)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)))*log(-sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) - d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 3*(c*cos(f*x + e) + d*sin(f*x + e))*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3))/(d*f*cos(f*x + e))","B",0
684,1,2793,0,1.967943," ","integrate(tan(f*x+e)*(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{2 \, f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) \log\left(-2 \, f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 8 \, f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \arctan\left(\frac{\sqrt{-2 \, f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)}{{\left(c^{2} + d^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + 4 \, {\left(\sqrt{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \arctan\left(-\frac{2 \, \sqrt{3} f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + 2 \, {\left(f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + 2 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sqrt{\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} + \sqrt{3} {\left(c^{2} + d^{2}\right)}}{4 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)^{2} - c^{2} - d^{2}}\right) - 4 \, {\left(\sqrt{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \arctan\left(\frac{2 \, \sqrt{3} f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 2 \, {\left(f^{5} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + 2 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f^{5} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \sqrt{-\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} + \sqrt{3} {\left(c^{2} + d^{2}\right)}}{4 \, {\left(c^{2} + d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)^{2} - c^{2} - d^{2}}\right) - {\left(\sqrt{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \log\left(\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + {\left(\sqrt{3} f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) - f \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right)\right)} \log\left(-\sqrt{3} f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{{\left(f^{6} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} - c f^{3}\right)} \sqrt{\frac{d^{2}}{f^{6}}}}{d^{2}}\right)\right) + f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 12 \, \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}}}{4 \, f}"," ",0,"1/4*(2*f*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2))*log(-2*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 8*f*((c^2 + d^2)/f^6)^(1/6)*arctan((sqrt(-2*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3))*f^5*((c^2 + d^2)/f^6)^(5/6) - f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6) + (c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))/((c^2 + d^2)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2))))*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + 4*(sqrt(3)*f*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) - f*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*arctan(-(2*sqrt(3)*f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + 2*(f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6) + 2*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) - 2*(sqrt(3)*f^5*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^5*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*sqrt(sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + sqrt(3)*(c^2 + d^2))/(4*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2))^2 - c^2 - d^2)) - 4*(sqrt(3)*f*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*arctan((2*sqrt(3)*f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) - 2*(f^5*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(5/6) + 2*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) - 2*(sqrt(3)*f^5*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) - f^5*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*sqrt(-sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + sqrt(3)*(c^2 + d^2))/(4*(c^2 + d^2)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2))^2 - c^2 - d^2)) - (sqrt(3)*f*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*log(sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + (sqrt(3)*f*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) - f*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)))*log(-sqrt(3)*f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt((c^2 + d^2)/f^6) - c*f^3)*sqrt(d^2/f^6)/d^2)) + f^2*((c^2 + d^2)/f^6)^(1/3) + ((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 12*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3))/f","B",0
685,1,3320,0,2.778104," ","integrate((c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) \log\left(2 \, c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + 2 \, \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \arctan\left(-\frac{c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - \sqrt{2 \, c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + {\left(c^{4} + c^{2} d^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)}{{\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + {\left(\sqrt{3} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \arctan\left(-\frac{2 \, c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - 2 \, {\left(\sqrt{3} c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 2 \, {\left(\sqrt{3} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sqrt{\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} + \sqrt{3} {\left(c^{4} + c^{2} d^{2}\right)}}{3 \, c^{4} + 3 \, c^{2} d^{2} - 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)^{2}}\right) + {\left(\sqrt{3} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \arctan\left(\frac{2 \, c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + 2 \, {\left(\sqrt{3} c f^{8} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} - 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - 2 \, {\left(\sqrt{3} f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + f^{8} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \sqrt{-\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}} - \sqrt{3} {\left(c^{4} + c^{2} d^{2}\right)}}{3 \, c^{4} + 3 \, c^{2} d^{2} - 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)^{2}}\right) - \frac{1}{4} \, {\left(\sqrt{3} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \log\left(\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right) + \frac{1}{4} \, {\left(\sqrt{3} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right)\right)} \log\left(-\sqrt{3} c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) - c f^{4} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{1}{3}} \sqrt{\frac{c^{2}}{f^{6}}} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{f^{6} \sqrt{\frac{c^{2}}{f^{6}}} \sqrt{\frac{c^{2} + d^{2}}{f^{6}}} + d f^{3} \sqrt{\frac{c^{2}}{f^{6}}}}{c^{2}}\right)\right) + c^{2} f^{2} \left(\frac{c^{2} + d^{2}}{f^{6}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{\frac{2}{3}}\right)"," ",0,"1/2*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))*log(2*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 2*((c^2 + d^2)/f^6)^(1/6)*arctan(-(c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) - sqrt(2*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3))*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) + (c^4 + c^2*d^2)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))/((c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + (sqrt(3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - ((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*arctan(-(2*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - 2*(sqrt(3)*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) + 2*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + 2*(sqrt(3)*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sqrt(sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + sqrt(3)*(c^4 + c^2*d^2))/(3*c^4 + 3*c^2*d^2 - 4*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))^2)) + (sqrt(3)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + ((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*arctan((2*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + 2*(sqrt(3)*c*f^8*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6) - 2*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - 2*(sqrt(3)*f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + f^8*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(5/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*sqrt(-sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) - sqrt(3)*(c^4 + c^2*d^2))/(3*c^4 + 3*c^2*d^2 - 4*(c^4 + c^2*d^2)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2))^2)) - 1/4*(sqrt(3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + ((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*log(sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3)) + 1/4*(sqrt(3)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - ((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)))*log(-sqrt(3)*c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*cos(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) - c*f^4*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(1/3)*sqrt(c^2/f^6)*((c^2 + d^2)/f^6)^(1/6)*sin(2/3*arctan((f^6*sqrt(c^2/f^6)*sqrt((c^2 + d^2)/f^6) + d*f^3*sqrt(c^2/f^6))/c^2)) + c^2*f^2*((c^2 + d^2)/f^6)^(1/3) + c^2*((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))^(2/3))","B",0
686,-1,0,0,0.000000," ","integrate(cot(f*x+e)*(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
687,1,25,0,1.650241," ","integrate(cot(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","-\frac{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}}}{f \tan\left(f x + e\right)}"," ",0,"-(d*tan(f*x + e) + c)^(1/3)/(f*tan(f*x + e))","A",0
688,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,1,3320,0,2.136900," ","integrate((a+b*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) \log\left(2 \, a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + a^{2} d^{2} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + 2 \, \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \arctan\left(-\frac{a d^{8} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} - \sqrt{2 \, a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + a^{2} d^{2} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} d^{8} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} + {\left(a^{4} + a^{2} b^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)}{{\left(a^{4} + a^{2} b^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + {\left(\sqrt{3} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \arctan\left(-\frac{2 \, a d^{8} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - 2 \, {\left(\sqrt{3} a d^{8} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + 2 \, {\left(\sqrt{3} d^{8} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - d^{8} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \sqrt{\sqrt{3} a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + a^{2} d^{2} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} + \sqrt{3} {\left(a^{4} + a^{2} b^{2}\right)}}{3 \, a^{4} + 3 \, a^{2} b^{2} - 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)^{2}}\right) + {\left(\sqrt{3} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \arctan\left(\frac{2 \, a d^{8} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + 2 \, {\left(\sqrt{3} a d^{8} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - 2 \, {\left(\sqrt{3} d^{8} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + d^{8} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{5}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \sqrt{-\sqrt{3} a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + a^{2} d^{2} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} - \sqrt{3} {\left(a^{4} + a^{2} b^{2}\right)}}{3 \, a^{4} + 3 \, a^{2} b^{2} - 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)^{2}}\right) - \frac{1}{4} \, {\left(\sqrt{3} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \log\left(\sqrt{3} a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + a^{2} d^{2} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + \frac{1}{4} \, {\left(\sqrt{3} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right)\right)} \log\left(-\sqrt{3} a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) - a d^{4} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \sqrt{\frac{a^{2}}{d^{6}}} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{d^{6} \sqrt{\frac{a^{2}}{d^{6}}} \sqrt{\frac{a^{2} + b^{2}}{d^{6}}} + b d^{3} \sqrt{\frac{a^{2}}{d^{6}}}}{a^{2}}\right)\right) + a^{2} d^{2} \left(\frac{a^{2} + b^{2}}{d^{6}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right)"," ",0,"1/2*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2))*log(2*a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + a^2*d^2*((a^2 + b^2)/d^6)^(1/3) + a^2*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(2/3)) + 2*((a^2 + b^2)/d^6)^(1/6)*arctan(-(a*d^8*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6) - sqrt(2*a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + a^2*d^2*((a^2 + b^2)/d^6)^(1/3) + a^2*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(2/3))*d^8*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6) + (a^4 + a^2*b^2)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))/((a^4 + a^2*b^2)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2))))*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + (sqrt(3)*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - ((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*arctan(-(2*a*d^8*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - 2*(sqrt(3)*a*d^8*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6) + 2*(a^4 + a^2*b^2)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + 2*(sqrt(3)*d^8*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - d^8*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*sqrt(sqrt(3)*a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + a^2*d^2*((a^2 + b^2)/d^6)^(1/3) + a^2*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(2/3)) + sqrt(3)*(a^4 + a^2*b^2))/(3*a^4 + 3*a^2*b^2 - 4*(a^4 + a^2*b^2)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2))^2)) + (sqrt(3)*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + ((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*arctan((2*a*d^8*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + 2*(sqrt(3)*a*d^8*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6) - 2*(a^4 + a^2*b^2)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - 2*(sqrt(3)*d^8*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + d^8*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(5/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*sqrt(-sqrt(3)*a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + a^2*d^2*((a^2 + b^2)/d^6)^(1/3) + a^2*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(2/3)) - sqrt(3)*(a^4 + a^2*b^2))/(3*a^4 + 3*a^2*b^2 - 4*(a^4 + a^2*b^2)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2))^2)) - 1/4*(sqrt(3)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + ((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*log(sqrt(3)*a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + a^2*d^2*((a^2 + b^2)/d^6)^(1/3) + a^2*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(2/3)) + 1/4*(sqrt(3)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - ((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)))*log(-sqrt(3)*a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*cos(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) - a*d^4*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(1/3)*sqrt(a^2/d^6)*((a^2 + b^2)/d^6)^(1/6)*sin(2/3*arctan((d^6*sqrt(a^2/d^6)*sqrt((a^2 + b^2)/d^6) + b*d^3*sqrt(a^2/d^6))/a^2)) + a^2*d^2*((a^2 + b^2)/d^6)^(1/3) + a^2*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^(2/3))","B",0
692,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,0,0,0,1.246454," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} \tan\left(f x + e\right)^{4} + 4 \, a b^{3} \tan\left(f x + e\right)^{3} + 6 \, a^{2} b^{2} \tan\left(f x + e\right)^{2} + 4 \, a^{3} b \tan\left(f x + e\right) + a^{4}\right)} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^4*tan(f*x + e)^4 + 4*a*b^3*tan(f*x + e)^3 + 6*a^2*b^2*tan(f*x + e)^2 + 4*a^3*b*tan(f*x + e) + a^4)*(d*tan(f*x + e))^n, x)","F",0
697,0,0,0,0.975651," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*(d*tan(f*x + e))^n, x)","F",0
698,0,0,0,0.859892," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*tan(f*x + e))^n, x)","F",0
699,0,0,0,1.073472," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
700,0,0,0,1.794060," ","integrate((d*tan(f*x+e))^n/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \tan\left(f x + e\right)\right)^{n}}{b \tan\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*tan(f*x + e))^n/(b*tan(f*x + e) + a), x)","F",0
701,0,0,0,2.005999," ","integrate((d*tan(f*x+e))^n/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \tan\left(f x + e\right)\right)^{n}}{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*tan(f*x + e))^n/(b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2), x)","F",0
702,0,0,0,2.878607," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^m, x)","F",0
703,0,0,0,1.900175," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}, x\right)"," ",0,"integral(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
704,0,0,0,1.117153," ","integrate(tan(d*x+c)^m/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(d x + c\right)^{m}}{\sqrt{b \tan\left(d x + c\right) + a}}, x\right)"," ",0,"integral(tan(d*x + c)^m/sqrt(b*tan(d*x + c) + a), x)","F",0
705,0,0,0,2.044161," ","integrate(tan(d*x+c)^m/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}}{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m/(b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) + a^2), x)","F",0
706,0,0,0,0.776757," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
707,0,0,0,1.036016," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
708,0,0,0,1.856226," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
709,0,0,0,0.927228," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
710,0,0,0,2.694566," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right), x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*tan(d*x + c), x)","F",0
711,0,0,0,0.843971," ","integrate((a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n, x)","F",0
712,0,0,0,1.710830," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right), x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cot(d*x + c), x)","F",0
713,0,0,0,1.649890," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
714,0,0,0,0.956490," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
715,0,0,0,0.840801," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
716,0,0,0,0.815676," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \sqrt{\tan\left(d x + c\right)}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
717,0,0,0,0.778086," ","integrate((a+b*tan(d*x+c))^n/tan(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{\tan\left(d x + c\right)}}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
718,0,0,0,1.083405," ","integrate((a+b*tan(d*x+c))^n/tan(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
719,1,287,0,0.928946," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - {\left(-32 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"-1/12*(3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-4*I*a^2/d^2)*log(((I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-4*I*a^2/d^2)*log(((-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - (-32*I*a*e^(2*I*d*x + 2*I*c) + 16*I*a)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
720,1,228,0,0.809790," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{d \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - d \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \log\left(-\frac{{\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - 8 \, a \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{4 \, d}"," ",0,"1/4*(d*sqrt(4*I*a^2/d^2)*log(((d*e^(2*I*d*x + 2*I*c) - d)*sqrt(4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - d*sqrt(4*I*a^2/d^2)*log(-((d*e^(2*I*d*x + 2*I*c) - d)*sqrt(4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - 8*a*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/d","C",0
721,1,191,0,2.768771," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - \frac{1}{4} \, \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right)"," ",0,"1/4*sqrt(-4*I*a^2/d^2)*log(((I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - 1/4*sqrt(-4*I*a^2/d^2)*log(((-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a)","C",0
722,1,278,0,1.655415," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \log\left(-\frac{{\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - 8 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} - a\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/4*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(4*I*a^2/d^2)*log(((d*e^(2*I*d*x + 2*I*c) - d)*sqrt(4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(4*I*a^2/d^2)*log(-((d*e^(2*I*d*x + 2*I*c) - d)*sqrt(4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - 8*(a*e^(2*I*d*x + 2*I*c) - a)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
723,1,329,0,2.053705," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - 3 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \log\left(\frac{{\left({\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{4 i \, a^{2}}{d^{2}}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - {\left(-32 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/12*(3*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-4*I*a^2/d^2)*log(((I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - 3*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-4*I*a^2/d^2)*log(((-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-4*I*a^2/d^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 2*I*a*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)/a) - (-32*I*a*e^(4*I*d*x + 4*I*c) + 16*I*a*e^(2*I*d*x + 2*I*c) + 16*I*a)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
724,1,340,0,2.009977," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - 15 \, \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - 8 \, {\left(43 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 54 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 23 \, a^{2}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{60 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/60*(15*sqrt(16*I*a^4/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - 15*sqrt(16*I*a^4/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) - sqrt(16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - 8*(43*a^2*e^(4*I*d*x + 4*I*c) - 54*a^2*e^(2*I*d*x + 2*I*c) + 23*a^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
725,1,297,0,0.583029," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - 3 \, \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - {\left(-56 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 40 i \, a^{2}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"-1/12*(3*sqrt(-16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(-16*I*a^4/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - 3*sqrt(-16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(-16*I*a^4/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - (-56*I*a^2*e^(2*I*d*x + 2*I*c) + 40*I*a^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
726,1,236,0,2.220417," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a^{2} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - \sqrt{\frac{16 i \, a^{4}}{d^{2}}} d \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) + \sqrt{\frac{16 i \, a^{4}}{d^{2}}} d \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right)}{4 \, d}"," ",0,"-1/4*(8*a^2*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - sqrt(16*I*a^4/d^2)*d*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) + sqrt(16*I*a^4/d^2)*d*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) - sqrt(16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2))/d","C",0
727,1,289,0,0.849689," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) + {\left(8 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{2}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(-16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(-16*I*a^4/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - sqrt(-16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(-16*I*a^4/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) + (8*I*a^2*e^(2*I*d*x + 2*I*c) - 8*I*a^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(2*I*d*x + 2*I*c) + d)","C",0
728,1,340,0,0.620764," ","integrate((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - 3 \, \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - 8 \, {\left(7 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 \, a^{2}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/12*(3*sqrt(16*I*a^4/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - 3*sqrt(16*I*a^4/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) - sqrt(16*I*a^4/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - 8*(7*a^2*e^(4*I*d*x + 4*I*c) - 2*a^2*e^(2*I*d*x + 2*I*c) - 5*a^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
729,1,391,0,2.135200," ","integrate((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - 15 \, \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{16 i \, a^{4}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2}}\right) - {\left(-344 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 88 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 248 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 184 i \, a^{2}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{60 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/60*(15*sqrt(-16*I*a^4/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(-16*I*a^4/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - 15*sqrt(-16*I*a^4/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/2*(4*I*a^2*e^(2*I*d*x + 2*I*c) + sqrt(-16*I*a^4/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^2) - (-344*I*a^2*e^(6*I*d*x + 6*I*c) - 88*I*a^2*e^(4*I*d*x + 4*I*c) + 248*I*a^2*e^(2*I*d*x + 2*I*c) + 184*I*a^2)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
730,1,340,0,2.078530," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5 \, \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - 5 \, \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - 16 \, {\left(13 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 19 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 \, a^{3}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{20 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/20*(5*sqrt(64*I*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - 5*sqrt(64*I*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) - sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - 16*(13*a^3*e^(4*I*d*x + 4*I*c) - 19*a^3*e^(2*I*d*x + 2*I*c) + 8*a^3)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
731,1,297,0,0.681999," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - 3 \, \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - {\left(-80 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i \, a^{3}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"-1/12*(3*sqrt(-64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(-64*I*a^6/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - 3*sqrt(-64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(-64*I*a^6/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - (-80*I*a^3*e^(2*I*d*x + 2*I*c) + 64*I*a^3)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
732,1,281,0,1.108548," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, a^{3} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) + \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/4*(16*a^3*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*e^(2*I*d*x + 2*I*c) - sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) + sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) - sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
733,1,340,0,2.699670," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - 3 \, \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{-\frac{64 i \, a^{6}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) + {\left(80 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 16 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 64 i \, a^{3}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/12*(3*sqrt(-64*I*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(-64*I*a^6/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - 3*sqrt(-64*I*a^6/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(-64*I*a^6/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) + (80*I*a^3*e^(4*I*d*x + 4*I*c) - 16*I*a^3*e^(2*I*d*x + 2*I*c) - 64*I*a^3)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
734,1,390,0,0.716270," ","integrate((a+I*a*tan(d*x+c))^3/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - 5 \, \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - \sqrt{\frac{64 i \, a^{6}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3}}\right) - 16 \, {\left(13 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 11 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 8 \, a^{3}\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}}{20 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-1/20*(5*sqrt(64*I*a^6/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) + sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - 5*sqrt(64*I*a^6/d^2)*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(8*I*a^3*e^(2*I*d*x + 2*I*c) - sqrt(64*I*a^6/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a^3) - 16*(13*a^3*e^(6*I*d*x + 6*I*c) + 6*a^3*e^(4*I*d*x + 4*I*c) - 11*a^3*e^(2*I*d*x + 2*I*c) - 8*a^3)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
735,1,469,0,1.124140," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(2 \, {\left(2 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - a d \sqrt{\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-2 \, {\left(2 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + a d \sqrt{-\frac{4 i}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a^{2} d^{2}}} + 2 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - a d \sqrt{-\frac{4 i}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a^{2} d^{2}}} - 2 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(9 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(2*(2*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/4*I/(a^2*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - a*d*sqrt(1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-2*(2*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/4*I/(a^2*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + a*d*sqrt(-4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a^2*d^2)) + 2*I)*e^(-2*I*d*x - 2*I*c)/(a*d)) - a*d*sqrt(-4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a^2*d^2)) - 2*I)*e^(-2*I*d*x - 2*I*c)/(a*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(9*e^(2*I*d*x + 2*I*c) - 1))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
736,1,466,0,0.645452," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left({\left({\left(4 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - a d \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left({\left({\left(-4 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - a d \sqrt{\frac{i}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{a^{2} d^{2}}} + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + a d \sqrt{\frac{i}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{a^{2} d^{2}}} - 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(-1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((4*I*a*d*e^(2*I*d*x + 2*I*c) - 4*I*a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/4*I/(a^2*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - a*d*sqrt(-1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((-4*I*a*d*e^(2*I*d*x + 2*I*c) + 4*I*a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/4*I/(a^2*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - a*d*sqrt(I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(I/(a^2*d^2)) + 1)*e^(-2*I*d*x - 2*I*c)/(a*d)) + a*d*sqrt(I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(I/(a^2*d^2)) - 1)*e^(-2*I*d*x - 2*I*c)/(a*d)) + sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-I*e^(2*I*d*x + 2*I*c) + I))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
737,1,269,0,1.158429," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(2 \, {\left(2 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - a d \sqrt{\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-2 \, {\left(2 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(2*(2*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/4*I/(a^2*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - a*d*sqrt(1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-2*(2*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/4*I/(a^2*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(e^(2*I*d*x + 2*I*c) - 1))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
738,1,467,0,1.108634," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left({\left({\left(4 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - a d \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left({\left({\left(-4 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{4 \, a^{2} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + a d \sqrt{\frac{i}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{a^{2} d^{2}}} + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - a d \sqrt{\frac{i}{a^{2} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{a^{2} d^{2}}} - 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(-1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((4*I*a*d*e^(2*I*d*x + 2*I*c) - 4*I*a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/4*I/(a^2*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - a*d*sqrt(-1/4*I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((-4*I*a*d*e^(2*I*d*x + 2*I*c) + 4*I*a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/4*I/(a^2*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + a*d*sqrt(I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(-((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(I/(a^2*d^2)) + 1)*e^(-2*I*d*x - 2*I*c)/(a*d)) - a*d*sqrt(I/(a^2*d^2))*e^(2*I*d*x + 2*I*c)*log(((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(I/(a^2*d^2)) - 1)*e^(-2*I*d*x - 2*I*c)/(a*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(I*e^(2*I*d*x + 2*I*c) - I))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
739,1,548,0,0.632670," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} \log\left(2 \, {\left(2 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} \log\left(-2 \, {\left(2 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{4 \, a^{2} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{-\frac{4 i}{a^{2} d^{2}}} \log\left(-\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a^{2} d^{2}}} + 2 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) + {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{-\frac{4 i}{a^{2} d^{2}}} \log\left(\frac{{\left({\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a^{2} d^{2}}} - 2 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(9 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 8 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}}{4 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/4*((a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/4*I/(a^2*d^2))*log(2*(2*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/4*I/(a^2*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - (a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(1/4*I/(a^2*d^2))*log(-2*(2*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/4*I/(a^2*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - (a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(-4*I/(a^2*d^2))*log(-((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a^2*d^2)) + 2*I)*e^(-2*I*d*x - 2*I*c)/(a*d)) + (a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))*sqrt(-4*I/(a^2*d^2))*log(((a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a^2*d^2)) - 2*I)*e^(-2*I*d*x - 2*I*c)/(a*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(9*e^(4*I*d*x + 4*I*c) - 8*e^(2*I*d*x + 2*I*c) - 1))/(a*d*e^(4*I*d*x + 4*I*c) + a*d*e^(2*I*d*x + 2*I*c))","B",0
740,1,509,0,0.976676," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} d \sqrt{\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(2 \, {\left(4 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{16 \, a^{4} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-2 \, {\left(4 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{16 \, a^{4} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 4 \, a^{2} d \sqrt{-\frac{529 i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{529 i}{64 \, a^{4} d^{2}}} + 23 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 4 \, a^{2} d \sqrt{-\frac{529 i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{529 i}{64 \, a^{4} d^{2}}} - 23 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(42 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 9 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*a^2*d*sqrt(1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*(4*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/16*I/(a^4*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*(4*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/16*I/(a^4*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + 4*a^2*d*sqrt(-529/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-529/64*I/(a^4*d^2)) + 23*I)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 4*a^2*d*sqrt(-529/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-529/64*I/(a^4*d^2)) - 23*I)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(42*e^(4*I*d*x + 4*I*c) - 9*e^(2*I*d*x + 2*I*c) - 1))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
741,1,506,0,1.787335," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} d \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left({\left({\left(8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left({\left({\left(-8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{\frac{49 i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{49 i}{64 \, a^{4} d^{2}}} + 7\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 4 \, a^{2} d \sqrt{\frac{49 i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{49 i}{64 \, a^{4} d^{2}}} - 7\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-6 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*a^2*d*sqrt(-1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(((8*I*a^2*d*e^(2*I*d*x + 2*I*c) - 8*I*a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/16*I/(a^4*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(-1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(((-8*I*a^2*d*e^(2*I*d*x + 2*I*c) + 8*I*a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/16*I/(a^4*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(49/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(49/64*I/(a^4*d^2)) + 7)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 4*a^2*d*sqrt(49/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(49/64*I/(a^4*d^2)) - 7)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-6*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(2*I*d*x + 2*I*c) + I))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
742,1,509,0,2.973057," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{2} d \sqrt{\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(2 \, {\left(4 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{16 \, a^{4} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-2 \, {\left(4 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{16 \, a^{4} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{-\frac{i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{4} d^{2}}} + i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 4 \, a^{2} d \sqrt{-\frac{i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{4} d^{2}}} - i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(2 \, e^{\left(4 i \, d x + 4 i \, c\right)} - e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"-1/16*(4*a^2*d*sqrt(1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*(4*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/16*I/(a^4*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*(4*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/16*I/(a^4*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(-1/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^4*d^2)) + I)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 4*a^2*d*sqrt(-1/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^4*d^2)) - I)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(2*e^(4*I*d*x + 4*I*c) - e^(2*I*d*x + 2*I*c) - 1))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
743,1,507,0,1.756828," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{2} d \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left({\left({\left(8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left({\left({\left(-8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 4 \, a^{2} d \sqrt{\frac{i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{64 \, a^{4} d^{2}}} + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 4 \, a^{2} d \sqrt{\frac{i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{64 \, a^{4} d^{2}}} - 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-2 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"-1/16*(4*a^2*d*sqrt(-1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(((8*I*a^2*d*e^(2*I*d*x + 2*I*c) - 8*I*a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/16*I/(a^4*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(-1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(((-8*I*a^2*d*e^(2*I*d*x + 2*I*c) + 8*I*a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/16*I/(a^4*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + 4*a^2*d*sqrt(1/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/64*I/(a^4*d^2)) + 1)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 4*a^2*d*sqrt(1/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/64*I/(a^4*d^2)) - 1)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-2*I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c) - I))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
744,1,508,0,0.648627," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} d \sqrt{\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(2 \, {\left(4 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{16 \, a^{4} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, a^{2} d \sqrt{\frac{i}{16 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-2 \, {\left(4 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{16 \, a^{4} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 4 \, a^{2} d \sqrt{-\frac{49 i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{49 i}{64 \, a^{4} d^{2}}} + 7 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) - 4 \, a^{2} d \sqrt{-\frac{49 i}{64 \, a^{4} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{49 i}{64 \, a^{4} d^{2}}} - 7 i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(6 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 7 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*a^2*d*sqrt(1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(2*(4*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/16*I/(a^4*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*a^2*d*sqrt(1/16*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-2*(4*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/16*I/(a^4*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + 4*a^2*d*sqrt(-49/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-49/64*I/(a^4*d^2)) + 7*I)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) - 4*a^2*d*sqrt(-49/64*I/(a^4*d^2))*e^(4*I*d*x + 4*I*c)*log(-1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-49/64*I/(a^4*d^2)) - 7*I)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(6*e^(4*I*d*x + 4*I*c) - 7*e^(2*I*d*x + 2*I*c) + 1))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
745,1,597,0,1.420610," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} \log\left({\left({\left(8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} \log\left({\left({\left(-8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{16 \, a^{4} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 4 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{529 i}{64 \, a^{4} d^{2}}} \log\left(-\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{529 i}{64 \, a^{4} d^{2}}} + 23\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + 4 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \sqrt{\frac{529 i}{64 \, a^{4} d^{2}}} \log\left(\frac{{\left(8 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{529 i}{64 \, a^{4} d^{2}}} - 23\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{2} d}\right) + \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(42 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 33 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 10 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{16 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/16*(4*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(-1/16*I/(a^4*d^2))*log(((8*I*a^2*d*e^(2*I*d*x + 2*I*c) - 8*I*a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/16*I/(a^4*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(-1/16*I/(a^4*d^2))*log(((-8*I*a^2*d*e^(2*I*d*x + 2*I*c) + 8*I*a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/16*I/(a^4*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 4*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(529/64*I/(a^4*d^2))*log(-1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(529/64*I/(a^4*d^2)) + 23)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + 4*(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))*sqrt(529/64*I/(a^4*d^2))*log(1/8*(8*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(529/64*I/(a^4*d^2)) - 23)*e^(-2*I*d*x - 2*I*c)/(a^2*d)) + sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(42*I*e^(6*I*d*x + 6*I*c) - 33*I*e^(4*I*d*x + 4*I*c) - 10*I*e^(2*I*d*x + 2*I*c) + I))/(a^2*d*e^(6*I*d*x + 6*I*c) + a^2*d*e^(4*I*d*x + 4*I*c))","B",0
746,1,517,0,0.959269," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left({\left({\left(16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i \, a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left({\left({\left(-16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left(4 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} + 3\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3} d}\right) + 12 \, a^{3} d \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(4 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} - 3\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3} d}\right) + \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-20 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 14 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{48 \, a^{3} d}"," ",0,"1/48*(12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(((16*I*a^3*d*e^(2*I*d*x + 2*I*c) - 16*I*a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(((-16*I*a^3*d*e^(2*I*d*x + 2*I*c) + 16*I*a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(9/16*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/4*(4*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(9/16*I/(a^6*d^2)) + 3)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 12*a^3*d*sqrt(9/16*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/4*(4*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(9/16*I/(a^6*d^2)) - 3)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-20*I*e^(6*I*d*x + 6*I*c) + 14*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(2*I*d*x + 2*I*c) + I))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","B",0
747,1,518,0,0.966951," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, a^{3} d \sqrt{\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(2 \, {\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{64 \, a^{6} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-2 \, {\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{64 \, a^{6} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) + 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} - i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(2 \, e^{\left(6 i \, d x + 6 i \, c\right)} + e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{48 \, a^{3} d}"," ",0,"-1/48*(12*a^3*d*sqrt(1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(2*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/64*I/(a^6*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-2*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/64*I/(a^6*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + I)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) - I)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(2*e^(6*I*d*x + 6*I*c) + e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) - 1))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","B",0
748,1,304,0,0.959963," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left({\left({\left(16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i \, a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left({\left({\left(-16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-4 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{48 \, a^{3} d}"," ",0,"-1/48*(12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(((16*I*a^3*d*e^(2*I*d*x + 2*I*c) - 16*I*a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(((-16*I*a^3*d*e^(2*I*d*x + 2*I*c) + 16*I*a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-4*I*e^(6*I*d*x + 6*I*c) + 4*I*e^(4*I*d*x + 4*I*c) + I*e^(2*I*d*x + 2*I*c) - I))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","B",0
749,1,520,0,0.821947," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, a^{3} d \sqrt{\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(2 \, {\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{64 \, a^{6} d^{2}}} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-2 \, {\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{64 \, a^{6} d^{2}}} - i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left(8 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} - i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a^{3} d}\right) - \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(2 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 5 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{48 \, a^{3} d}"," ",0,"1/48*(12*a^3*d*sqrt(1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(2*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/64*I/(a^6*d^2)) + I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-2*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/64*I/(a^6*d^2)) - I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/8*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + I)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/8*(8*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) - I)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(2*e^(6*I*d*x + 6*I*c) - 5*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) - 1))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","B",0
750,1,517,0,0.763219," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left({\left({\left(16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i \, a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 12 \, a^{3} d \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left({\left({\left(-16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{64 \, a^{6} d^{2}}} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 12 \, a^{3} d \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(4 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} + 3\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3} d}\right) - 12 \, a^{3} d \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-\frac{{\left(4 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{9 i}{16 \, a^{6} d^{2}}} - 3\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3} d}\right) + \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-20 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 26 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{48 \, a^{3} d}"," ",0,"1/48*(12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(((16*I*a^3*d*e^(2*I*d*x + 2*I*c) - 16*I*a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) - 12*a^3*d*sqrt(-1/64*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(((-16*I*a^3*d*e^(2*I*d*x + 2*I*c) + 16*I*a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/64*I/(a^6*d^2)) + 2*I*e^(2*I*d*x + 2*I*c))*e^(-2*I*d*x - 2*I*c)) + 12*a^3*d*sqrt(9/16*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(1/4*(4*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(9/16*I/(a^6*d^2)) + 3)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) - 12*a^3*d*sqrt(9/16*I/(a^6*d^2))*e^(6*I*d*x + 6*I*c)*log(-1/4*(4*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(9/16*I/(a^6*d^2)) - 3)*e^(-2*I*d*x - 2*I*c)/(a^3*d)) + sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-20*I*e^(6*I*d*x + 6*I*c) + 26*I*e^(4*I*d*x + 4*I*c) - 7*I*e^(2*I*d*x + 2*I*c) + I))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","B",0
751,1,380,0,0.840442," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(17 \, e^{\left(5 i \, d x + 5 i \, c\right)} - 20 \, e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, e^{\left(i \, d x + i \, c\right)}\right)} - 15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{8 i \, a}{d^{2}}} \log\left(-{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{8 i \, a}{d^{2}}} - 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{60 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/60*(8*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(17*e^(5*I*d*x + 5*I*c) - 20*e^(3*I*d*x + 3*I*c) + 15*e^(I*d*x + I*c)) - 15*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(8*I*a/d^2)*log((sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 15*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(8*I*a/d^2)*log(-(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(8*I*a/d^2) - 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
752,1,326,0,0.972315," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{-16 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/12*(-16*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*e^(3*I*d*x + 3*I*c) - 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-8*I*a/d^2)*log((sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-8*I*a/d^2)*log((sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
753,1,282,0,1.723083," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} e^{\left(i \, d x + i \, c\right)} - d \sqrt{\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + d \sqrt{\frac{8 i \, a}{d^{2}}} \log\left(-{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{8 i \, a}{d^{2}}} - 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{4 \, d}"," ",0,"-1/4*(8*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*e^(I*d*x + I*c) - d*sqrt(8*I*a/d^2)*log((sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + d*sqrt(8*I*a/d^2)*log(-(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(8*I*a/d^2) - 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/d","B",0
754,1,217,0,0.878092," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \frac{1}{4} \, \sqrt{-\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)"," ",0,"1/4*sqrt(-8*I*a/d^2)*log((sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 1/4*sqrt(-8*I*a/d^2)*log((sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c))","B",0
755,1,468,0,0.916299," ","integrate((a+I*a*tan(d*x+c))^(1/2)/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \frac{1}{4} \, \sqrt{\frac{8 i \, a}{d^{2}}} \log\left(-{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{8 i \, a}{d^{2}}} - 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \frac{1}{4} \, \sqrt{\frac{4 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(16 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} - 16 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{4 i \, a}{d^{2}}} - 48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \frac{1}{4} \, \sqrt{\frac{4 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(-16 i \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 16 i \, a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{4 i \, a}{d^{2}}} - 48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)"," ",0,"-1/4*sqrt(8*I*a/d^2)*log((sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 1/4*sqrt(8*I*a/d^2)*log(-(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(8*I*a/d^2) - 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 1/4*sqrt(4*I*a/d^2)*log((sqrt(2)*(16*I*a*d*e^(3*I*d*x + 3*I*c) - 16*I*a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(4*I*a/d^2) - 48*a^2*e^(2*I*d*x + 2*I*c) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) - 1/4*sqrt(4*I*a/d^2)*log((sqrt(2)*(-16*I*a*d*e^(3*I*d*x + 3*I*c) + 16*I*a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(4*I*a/d^2) - 48*a^2*e^(2*I*d*x + 2*I*c) + 16*a^2)*e^(-2*I*d*x - 2*I*c))","B",0
756,1,609,0,1.800785," ","integrate((a+I*a*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-4 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 4 i \, e^{\left(i \, d x + i \, c\right)}\right)} - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{8 i \, a}{d^{2}}} \log\left({\left(\sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{8 i \, a}{d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{i \, a}{d^{2}}} \log\left(-16 \, {\left(2 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i \, a}{d^{2}}} + 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{i \, a}{d^{2}}} \log\left(16 \, {\left(2 \, \sqrt{2} {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i \, a}{d^{2}}} - 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-4*I*e^(3*I*d*x + 3*I*c) + 4*I*e^(I*d*x + I*c)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a/d^2)*log((sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-8*I*a/d^2)*log((sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-8*I*a/d^2) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-I*a/d^2)*log(-16*(2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-I*a/d^2) + 3*a^2*e^(2*I*d*x + 2*I*c) - a^2)*e^(-2*I*d*x - 2*I*c)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-I*a/d^2)*log(16*(2*sqrt(2)*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-I*a/d^2) - 3*a^2*e^(2*I*d*x + 2*I*c) + a^2)*e^(-2*I*d*x - 2*I*c)))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
757,1,402,0,0.881287," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(9 \, a e^{\left(5 i \, d x + 5 i \, c\right)} - 10 \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 5 \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 5 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + 5 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \log\left(-\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{20 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/20*(8*sqrt(2)*(9*a*e^(5*I*d*x + 5*I*c) - 10*a*e^(3*I*d*x + 3*I*c) + 5*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 5*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(32*I*a^3/d^2)*log(1/2*(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 5*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*sqrt(32*I*a^3/d^2)*log(-1/2*(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
758,1,361,0,1.487082," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-40 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 24 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/12*(sqrt(2)*(-40*I*a*e^(3*I*d*x + 3*I*c) + 24*I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-32*I*a^3/d^2)*log(1/2*(sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + 3*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(-32*I*a^3/d^2)*log(1/2*(sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
759,1,302,0,0.945794," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} a \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} e^{\left(i \, d x + i \, c\right)} - \sqrt{\frac{32 i \, a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + \sqrt{\frac{32 i \, a^{3}}{d^{2}}} d \log\left(-\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{4 \, d}"," ",0,"-1/4*(8*sqrt(2)*a*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*e^(I*d*x + I*c) - sqrt(32*I*a^3/d^2)*d*log(1/2*(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + sqrt(32*I*a^3/d^2)*d*log(-1/2*(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/d","B",0
760,1,491,0,0.528072," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} \log\left(-16 \, {\left(\sqrt{2} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} - d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \frac{1}{4} \, \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} \log\left(16 \, {\left(\sqrt{2} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} - d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{4 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \frac{1}{4} \, \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) - \frac{1}{4} \, \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{-\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)"," ",0,"-1/4*sqrt(-4*I*a^3/d^2)*log(-16*(sqrt(2)*(d*e^(3*I*d*x + 3*I*c) - d*e^(I*d*x + I*c))*sqrt(-4*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 3*a^2*e^(2*I*d*x + 2*I*c) - a^2)*e^(-2*I*d*x - 2*I*c)) + 1/4*sqrt(-4*I*a^3/d^2)*log(16*(sqrt(2)*(d*e^(3*I*d*x + 3*I*c) - d*e^(I*d*x + I*c))*sqrt(-4*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 3*a^2*e^(2*I*d*x + 2*I*c) + a^2)*e^(-2*I*d*x - 2*I*c)) + 1/4*sqrt(-32*I*a^3/d^2)*log(1/2*(sqrt(2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(-32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 1/4*sqrt(-32*I*a^3/d^2)*log(1/2*(sqrt(2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(-32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a)","B",0
761,1,635,0,4.130530," ","integrate((a+I*a*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(a e^{\left(3 i \, d x + 3 i \, c\right)} - a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{9 i \, a^{3}}{d^{2}}} \log\left(\frac{1}{3} \, {\left(\sqrt{2} {\left(32 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 32 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{9 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 144 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 48 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{9 i \, a^{3}}{d^{2}}} \log\left(\frac{1}{3} \, {\left(\sqrt{2} {\left(-32 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 32 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{9 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 144 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 48 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right) + {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \log\left(-\frac{{\left(\sqrt{2} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{32 i \, a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 8 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(4*sqrt(2)*(a*e^(3*I*d*x + 3*I*c) - a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(9*I*a^3/d^2)*log(1/3*(sqrt(2)*(32*I*d*e^(3*I*d*x + 3*I*c) - 32*I*d*e^(I*d*x + I*c))*sqrt(9*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 144*a^2*e^(2*I*d*x + 2*I*c) + 48*a^2)*e^(-2*I*d*x - 2*I*c)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(9*I*a^3/d^2)*log(1/3*(sqrt(2)*(-32*I*d*e^(3*I*d*x + 3*I*c) + 32*I*d*e^(I*d*x + I*c))*sqrt(9*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 144*a^2*e^(2*I*d*x + 2*I*c) + 48*a^2)*e^(-2*I*d*x - 2*I*c)) - (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(32*I*a^3/d^2)*log(1/2*(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + (d*e^(2*I*d*x + 2*I*c) + d)*sqrt(32*I*a^3/d^2)*log(-1/2*(sqrt(2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(32*I*a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 8*I*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
762,1,465,0,2.274720," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(640 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 1232 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 1120 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 336 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + 21 \, \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) - 21 \, \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{84 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} - 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/84*(sqrt(2)*(640*I*a^2*e^(7*I*d*x + 7*I*c) - 1232*I*a^2*e^(5*I*d*x + 5*I*c) + 1120*I*a^2*e^(3*I*d*x + 3*I*c) - 336*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + 21*sqrt(-128*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-128*I*a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2) - 21*sqrt(-128*I*a^5/d^2)*(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-128*I*a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2))/(d*e^(6*I*d*x + 6*I*c) - 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) - d)","B",0
763,1,409,0,1.116274," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{16 \, \sqrt{2} {\left(26 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 35 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 15 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 15 \, \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 15 \, \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{60 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/60*(16*sqrt(2)*(26*a^2*e^(5*I*d*x + 5*I*c) - 35*a^2*e^(3*I*d*x + 3*I*c) + 15*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 15*sqrt(128*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2) + 15*sqrt(128*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2))/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
764,1,365,0,0.712527," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-64 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 48 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - 3 \, \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + 3 \, \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{12 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)}}"," ",0,"1/12*(sqrt(2)*(-64*I*a^2*e^(3*I*d*x + 3*I*c) + 48*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - 3*sqrt(-128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-128*I*a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2) + 3*sqrt(-128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-128*I*a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2))/(d*e^(2*I*d*x + 2*I*c) - d)","B",0
765,1,572,0,0.895701," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} a^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} e^{\left(i \, d x + i \, c\right)} + \sqrt{\frac{4 i \, a^{5}}{d^{2}}} d \log\left(-\frac{{\left(48 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, a^{3} - \sqrt{2} \sqrt{\frac{4 i \, a^{5}}{d^{2}}} {\left(16 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 16 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - \sqrt{\frac{4 i \, a^{5}}{d^{2}}} d \log\left(-\frac{{\left(48 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 16 \, a^{3} - \sqrt{2} \sqrt{\frac{4 i \, a^{5}}{d^{2}}} {\left(-16 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 16 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a}\right) - \sqrt{\frac{128 i \, a^{5}}{d^{2}}} d \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + \sqrt{\frac{128 i \, a^{5}}{d^{2}}} d \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{4 \, d}"," ",0,"-1/4*(8*sqrt(2)*a^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*e^(I*d*x + I*c) + sqrt(4*I*a^5/d^2)*d*log(-(48*a^3*e^(2*I*d*x + 2*I*c) - 16*a^3 - sqrt(2)*sqrt(4*I*a^5/d^2)*(16*I*d*e^(3*I*d*x + 3*I*c) - 16*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a) - sqrt(4*I*a^5/d^2)*d*log(-(48*a^3*e^(2*I*d*x + 2*I*c) - 16*a^3 - sqrt(2)*sqrt(4*I*a^5/d^2)*(-16*I*d*e^(3*I*d*x + 3*I*c) + 16*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a) - sqrt(128*I*a^5/d^2)*d*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2) + sqrt(128*I*a^5/d^2)*d*log(1/4*(16*I*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2))/d","B",0
766,1,647,0,0.700661," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(4 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} - \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{16 \, {\left(15 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 \, a^{3} + 2 \, \sqrt{2} \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} - d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{5 \, a}\right) + \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{16 \, {\left(15 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 5 \, a^{3} - 2 \, \sqrt{2} \sqrt{-\frac{25 i \, a^{5}}{d^{2}}} {\left(d e^{\left(3 i \, d x + 3 i \, c\right)} - d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{5 \, a}\right) + \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) - \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{-\frac{128 i \, a^{5}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{4 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*(4*I*a^2*e^(3*I*d*x + 3*I*c) - 4*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) - sqrt(-25*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-16/5*(15*a^3*e^(2*I*d*x + 2*I*c) - 5*a^3 + 2*sqrt(2)*sqrt(-25*I*a^5/d^2)*(d*e^(3*I*d*x + 3*I*c) - d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a) + sqrt(-25*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(-16/5*(15*a^3*e^(2*I*d*x + 2*I*c) - 5*a^3 - 2*sqrt(2)*sqrt(-25*I*a^5/d^2)*(d*e^(3*I*d*x + 3*I*c) - d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a) + sqrt(-128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-128*I*a^5/d^2)*(I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2) - sqrt(-128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(-128*I*a^5/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
767,1,722,0,0.929184," ","integrate((a+I*a*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(11 \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 4 \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 7 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} + \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(1104 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 368 \, a^{3} - \sqrt{2} \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} {\left(128 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} - 128 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{23 \, a}\right) - \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(-\frac{{\left(1104 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 368 \, a^{3} - \sqrt{2} \sqrt{\frac{529 i \, a^{5}}{16 \, d^{2}}} {\left(-128 i \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 128 i \, d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{23 \, a}\right) - \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right) + \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{{\left(16 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - \sqrt{2} \sqrt{\frac{128 i \, a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} - d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{2}}\right)}{4 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/4*(sqrt(2)*(11*a^2*e^(5*I*d*x + 5*I*c) - 4*a^2*e^(3*I*d*x + 3*I*c) - 7*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)) + sqrt(529/16*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(-1/23*(1104*a^3*e^(2*I*d*x + 2*I*c) - 368*a^3 - sqrt(2)*sqrt(529/16*I*a^5/d^2)*(128*I*d*e^(3*I*d*x + 3*I*c) - 128*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a) - sqrt(529/16*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(-1/23*(1104*a^3*e^(2*I*d*x + 2*I*c) - 368*a^3 - sqrt(2)*sqrt(529/16*I*a^5/d^2)*(-128*I*d*e^(3*I*d*x + 3*I*c) + 128*I*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-2*I*d*x - 2*I*c)/a) - sqrt(128*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2) + sqrt(128*I*a^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/4*(16*I*a^3*e^(I*d*x + I*c) - sqrt(2)*sqrt(128*I*a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) - d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)))*e^(-I*d*x - I*c)/a^2))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
768,1,385,0,1.260379," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(14 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 36 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)} - 3 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{2 i}{a d^{2}}} \log\left({\left(\sqrt{2} {\left(2 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{2 i}{a d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{-\frac{2 i}{a d^{2}}} \log\left({\left(\sqrt{2} {\left(-2 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{2 i}{a d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{12 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/12*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(14*I*e^(4*I*d*x + 4*I*c) - 36*I*e^(2*I*d*x + 2*I*c) + 6*I) - 3*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(-2*I/(a*d^2))*log((sqrt(2)*(2*I*a*d*e^(2*I*d*x + 2*I*c) - 2*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-2*I/(a*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3*(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))*sqrt(-2*I/(a*d^2))*log((sqrt(2)*(-2*I*a*d*e^(2*I*d*x + 2*I*c) + 2*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-2*I/(a*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(a*d*e^(3*I*d*x + 3*I*c) - a*d*e^(I*d*x + I*c))","B",0
769,1,331,0,0.804257," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(2 \, {\left(\sqrt{2} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{2 i}{a d^{2}}} + 2 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-2 \, {\left(\sqrt{2} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{2 i}{a d^{2}}} - 2 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(5 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(2*(sqrt(2)*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(2*I/(a*d^2)) + 2*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(-2*(sqrt(2)*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(2*I/(a*d^2)) - 2*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(5*e^(2*I*d*x + 2*I*c) - 1))*e^(-I*d*x - I*c)/(a*d)","B",0
770,1,330,0,1.526179," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left({\left(\sqrt{2} {\left(2 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{2 i}{a d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left({\left(\sqrt{2} {\left(-2 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{2 i}{a d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log((sqrt(2)*(2*I*a*d*e^(2*I*d*x + 2*I*c) - 2*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-2*I/(a*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log((sqrt(2)*(-2*I*a*d*e^(2*I*d*x + 2*I*c) + 2*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-2*I/(a*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-2*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-I*d*x - I*c)/(a*d)","B",0
771,1,329,0,1.020433," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(2 \, {\left(\sqrt{2} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{2 i}{a d^{2}}} + 2 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - a d \sqrt{\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-2 \, {\left(\sqrt{2} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{2 i}{a d^{2}}} - 2 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(2*(sqrt(2)*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(2*I/(a*d^2)) + 2*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - a*d*sqrt(2*I/(a*d^2))*e^(I*d*x + I*c)*log(-2*(sqrt(2)*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(2*I/(a*d^2)) - 2*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(e^(2*I*d*x + 2*I*c) - 1))*e^(-I*d*x - I*c)/(a*d)","B",0
772,1,618,0,0.641866," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left({\left(\sqrt{2} {\left(2 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{2 i}{a d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - a d \sqrt{-\frac{2 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left({\left(\sqrt{2} {\left(-2 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{2 i}{a d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - a d \sqrt{-\frac{4 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-16 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a d^{2}}} + 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + a d \sqrt{-\frac{4 i}{a d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(16 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a d^{2}}} - 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"-1/4*(a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log((sqrt(2)*(2*I*a*d*e^(2*I*d*x + 2*I*c) - 2*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-2*I/(a*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - a*d*sqrt(-2*I/(a*d^2))*e^(I*d*x + I*c)*log((sqrt(2)*(-2*I*a*d*e^(2*I*d*x + 2*I*c) + 2*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-2*I/(a*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - a*d*sqrt(-4*I/(a*d^2))*e^(I*d*x + I*c)*log(-16*(sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) - a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a*d^2)) + 3*a^2*e^(2*I*d*x + 2*I*c) - a^2)*e^(-2*I*d*x - 2*I*c)) + a*d*sqrt(-4*I/(a*d^2))*e^(I*d*x + I*c)*log(16*(sqrt(2)*(a^2*d*e^(3*I*d*x + 3*I*c) - a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a*d^2)) - 3*a^2*e^(2*I*d*x + 2*I*c) + a^2)*e^(-2*I*d*x - 2*I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(2*I*e^(2*I*d*x + 2*I*c) - 2*I))*e^(-I*d*x - I*c)/(a*d)","B",0
773,1,699,0,0.821658," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(3 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)} - {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{2 i}{a d^{2}}} \log\left(2 \, {\left(\sqrt{2} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{2 i}{a d^{2}}} + 2 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{2 i}{a d^{2}}} \log\left(-2 \, {\left(\sqrt{2} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{2 i}{a d^{2}}} - 2 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{i}{a d^{2}}} \log\left({\left(\sqrt{2} {\left(32 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} - 32 i \, a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{a d^{2}}} - 48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{i}{a d^{2}}} \log\left({\left(\sqrt{2} {\left(-32 i \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + 32 i \, a^{2} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{a d^{2}}} - 48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)}{4 \, {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"-1/4*(2*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(3*e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) - 1) - (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(2*I/(a*d^2))*log(2*(sqrt(2)*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(2*I/(a*d^2)) + 2*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(2*I/(a*d^2))*log(-2*(sqrt(2)*(a*d*e^(2*I*d*x + 2*I*c) - a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(2*I/(a*d^2)) - 2*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(I/(a*d^2))*log((sqrt(2)*(32*I*a^2*d*e^(3*I*d*x + 3*I*c) - 32*I*a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(I/(a*d^2)) - 48*a^2*e^(2*I*d*x + 2*I*c) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) + (a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))*sqrt(I/(a*d^2))*log((sqrt(2)*(-32*I*a^2*d*e^(3*I*d*x + 3*I*c) + 32*I*a^2*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(I/(a*d^2)) - 48*a^2*e^(2*I*d*x + 2*I*c) + 16*a^2)*e^(-2*I*d*x - 2*I*c)))/(a*d*e^(3*I*d*x + 3*I*c) + a*d*e^(I*d*x + I*c))","B",0
774,1,416,0,0.926067," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(52 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 87 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 18 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} - 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} \log\left({\left(\sqrt{2} {\left(4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} \log\left({\left(\sqrt{2} {\left(-4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{12 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/12*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(52*I*e^(6*I*d*x + 6*I*c) - 87*I*e^(4*I*d*x + 4*I*c) + 18*I*e^(2*I*d*x + 2*I*c) + I) - 3*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-1/2*I/(a^3*d^2))*log((sqrt(2)*(4*I*a^2*d*e^(2*I*d*x + 2*I*c) - 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-1/2*I/(a^3*d^2))*log((sqrt(2)*(-4*I*a^2*d*e^(2*I*d*x + 2*I*c) + 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(3*I*d*x + 3*I*c))","B",0
775,1,355,0,0.802242," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} + i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(38 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 13 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/2*I/(a^3*d^2)) + I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/2*I/(a^3*d^2)) - I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(38*e^(4*I*d*x + 4*I*c) - 13*e^(2*I*d*x + 2*I*c) - 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
776,1,354,0,1.717869," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left({\left(\sqrt{2} {\left(4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left({\left(\sqrt{2} {\left(-4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-8 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*(4*I*a^2*d*e^(2*I*d*x + 2*I*c) - 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*(-4*I*a^2*d*e^(2*I*d*x + 2*I*c) + 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-8*I*e^(4*I*d*x + 4*I*c) + 7*I*e^(2*I*d*x + 2*I*c) + I))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
777,1,355,0,1.225007," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} + i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(2 \, e^{\left(4 i \, d x + 4 i \, c\right)} - e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/2*I/(a^3*d^2)) + I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/2*I/(a^3*d^2)) - I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(2*e^(4*I*d*x + 4*I*c) - e^(2*I*d*x + 2*I*c) - 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
778,1,355,0,1.626672," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left({\left(\sqrt{2} {\left(4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, a^{2} d \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left({\left(\sqrt{2} {\left(-4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"-1/12*(3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*(4*I*a^2*d*e^(2*I*d*x + 2*I*c) - 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*a^2*d*sqrt(-1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*(-4*I*a^2*d*e^(2*I*d*x + 2*I*c) + 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-4*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(2*I*d*x + 2*I*c) - I))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
779,1,648,0,0.621291," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} + i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, a^{2} d \sqrt{\frac{i}{2 \, a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{2 \, a^{3} d^{2}}} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, a^{2} d \sqrt{\frac{4 i}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left({\left(\sqrt{2} {\left(16 i \, a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} - 16 i \, a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{4 i}{a^{3} d^{2}}} - 48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 3 \, a^{2} d \sqrt{\frac{4 i}{a^{3} d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left({\left(\sqrt{2} {\left(-16 i \, a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + 16 i \, a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{4 i}{a^{3} d^{2}}} - 48 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(10 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 11 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a^{2} d}"," ",0,"1/12*(3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/2*I/(a^3*d^2)) + I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*a^2*d*sqrt(1/2*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*(a^2*d*e^(2*I*d*x + 2*I*c) - a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/2*I/(a^3*d^2)) - I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*a^2*d*sqrt(4*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*(16*I*a^3*d*e^(3*I*d*x + 3*I*c) - 16*I*a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(4*I/(a^3*d^2)) - 48*a^2*e^(2*I*d*x + 2*I*c) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) + 3*a^2*d*sqrt(4*I/(a^3*d^2))*e^(3*I*d*x + 3*I*c)*log((sqrt(2)*(-16*I*a^3*d*e^(3*I*d*x + 3*I*c) + 16*I*a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(4*I/(a^3*d^2)) - 48*a^2*e^(2*I*d*x + 2*I*c) + 16*a^2)*e^(-2*I*d*x - 2*I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(10*e^(4*I*d*x + 4*I*c) - 11*e^(2*I*d*x + 2*I*c) + 1))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","B",0
780,1,741,0,0.580850," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(28 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 13 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} + 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} \log\left({\left(\sqrt{2} {\left(4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} \log\left({\left(\sqrt{2} {\left(-4 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{2 \, a^{3} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{9 i}{a^{3} d^{2}}} \log\left(-\frac{16}{3} \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} - a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{9 i}{a^{3} d^{2}}} + 9 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) - 3 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \sqrt{-\frac{9 i}{a^{3} d^{2}}} \log\left(\frac{16}{3} \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} - a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{9 i}{a^{3} d^{2}}} - 9 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right)}{12 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/12*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(28*I*e^(6*I*d*x + 6*I*c) - 13*I*e^(4*I*d*x + 4*I*c) - 16*I*e^(2*I*d*x + 2*I*c) + I) + 3*(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-1/2*I/(a^3*d^2))*log((sqrt(2)*(4*I*a^2*d*e^(2*I*d*x + 2*I*c) - 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-1/2*I/(a^3*d^2))*log((sqrt(2)*(-4*I*a^2*d*e^(2*I*d*x + 2*I*c) + 4*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/2*I/(a^3*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3*(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-9*I/(a^3*d^2))*log(-16/3*(2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) - a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-9*I/(a^3*d^2)) + 9*a^2*e^(2*I*d*x + 2*I*c) - 3*a^2)*e^(-2*I*d*x - 2*I*c)) - 3*(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))*sqrt(-9*I/(a^3*d^2))*log(16/3*(2*sqrt(2)*(a^3*d*e^(3*I*d*x + 3*I*c) - a^3*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-9*I/(a^3*d^2)) - 9*a^2*e^(2*I*d*x + 2*I*c) + 3*a^2)*e^(-2*I*d*x - 2*I*c)))/(a^2*d*e^(5*I*d*x + 5*I*c) + a^2*d*e^(3*I*d*x + 3*I*c))","B",0
781,1,427,0,0.940049," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(983 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 1527 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 348 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 33 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} - 30 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} \log\left({\left(\sqrt{2} {\left(8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 30 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} \log\left({\left(\sqrt{2} {\left(-8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right)}{120 \, {\left(a^{3} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"1/120*(sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(983*I*e^(8*I*d*x + 8*I*c) - 1527*I*e^(6*I*d*x + 6*I*c) + 348*I*e^(4*I*d*x + 4*I*c) + 33*I*e^(2*I*d*x + 2*I*c) + 3*I) - 30*(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(-1/8*I/(a^5*d^2))*log((sqrt(2)*(8*I*a^3*d*e^(2*I*d*x + 2*I*c) - 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 30*(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))*sqrt(-1/8*I/(a^5*d^2))*log((sqrt(2)*(-8*I*a^3*d*e^(2*I*d*x + 2*I*c) + 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)))/(a^3*d*e^(7*I*d*x + 7*I*c) - a^3*d*e^(5*I*d*x + 5*I*c))","B",0
782,1,368,0,1.744179," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} + i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(463 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 194 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 26 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(2*sqrt(2)*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/8*I/(a^5*d^2)) + I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(2*sqrt(2)*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/8*I/(a^5*d^2)) - I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(463*e^(6*I*d*x + 6*I*c) - 194*e^(4*I*d*x + 4*I*c) - 26*e^(2*I*d*x + 2*I*c) - 3))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
783,1,365,0,0.949005," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left({\left(\sqrt{2} {\left(8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left({\left(\sqrt{2} {\left(-8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-83 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 64 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((sqrt(2)*(8*I*a^3*d*e^(2*I*d*x + 2*I*c) - 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((sqrt(2)*(-8*I*a^3*d*e^(2*I*d*x + 2*I*c) + 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-83*I*e^(6*I*d*x + 6*I*c) + 64*I*e^(4*I*d*x + 4*I*c) + 16*I*e^(2*I*d*x + 2*I*c) + 3*I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
784,1,366,0,0.781135," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(10 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} + i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 10 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 2 \, e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{3} d}"," ",0,"-1/40*(10*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(2*sqrt(2)*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/8*I/(a^5*d^2)) + I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 10*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(2*sqrt(2)*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/8*I/(a^5*d^2)) - I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(e^(6*I*d*x + 6*I*c) + 2*e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) - 1))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
785,1,366,0,0.911355," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left({\left(\sqrt{2} {\left(8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 30 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left({\left(\sqrt{2} {\left(-8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-17 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 16 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"-1/120*(30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((sqrt(2)*(8*I*a^3*d*e^(2*I*d*x + 2*I*c) - 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 30*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((sqrt(2)*(-8*I*a^3*d*e^(2*I*d*x + 2*I*c) + 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-17*I*e^(6*I*d*x + 6*I*c) + 16*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) - 3*I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
786,1,368,0,1.811761," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} + i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 30 \, a^{3} d \sqrt{\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(2 \, \sqrt{2} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{\frac{i}{8 \, a^{5} d^{2}}} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(23 \, e^{\left(6 i \, d x + 6 i \, c\right)} - 34 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 14 \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{120 \, a^{3} d}"," ",0,"1/120*(30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(2*sqrt(2)*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/8*I/(a^5*d^2)) + I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 30*a^3*d*sqrt(1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(2*sqrt(2)*(a^3*d*e^(2*I*d*x + 2*I*c) - a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(1/8*I/(a^5*d^2)) - I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(23*e^(6*I*d*x + 6*I*c) - 34*e^(4*I*d*x + 4*I*c) + 14*e^(2*I*d*x + 2*I*c) - 3))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
787,1,657,0,0.631270," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(10 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left({\left(\sqrt{2} {\left(8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 10 \, a^{3} d \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left({\left(\sqrt{2} {\left(-8 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{i}{8 \, a^{5} d^{2}}} + 4 i \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 10 \, a^{3} d \sqrt{-\frac{4 i}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-16 \, {\left(\sqrt{2} {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} - a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a^{5} d^{2}}} + 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + 10 \, a^{3} d \sqrt{-\frac{4 i}{a^{5} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(16 \, {\left(\sqrt{2} {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} - a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} \sqrt{-\frac{4 i}{a^{5} d^{2}}} - 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-41 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 48 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{3} d}"," ",0,"1/40*(10*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((sqrt(2)*(8*I*a^3*d*e^(2*I*d*x + 2*I*c) - 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 10*a^3*d*sqrt(-1/8*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log((sqrt(2)*(-8*I*a^3*d*e^(2*I*d*x + 2*I*c) + 8*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-1/8*I/(a^5*d^2)) + 4*I*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 10*a^3*d*sqrt(-4*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(-16*(sqrt(2)*(a^4*d*e^(3*I*d*x + 3*I*c) - a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a^5*d^2)) + 3*a^2*e^(2*I*d*x + 2*I*c) - a^2)*e^(-2*I*d*x - 2*I*c)) + 10*a^3*d*sqrt(-4*I/(a^5*d^2))*e^(5*I*d*x + 5*I*c)*log(16*(sqrt(2)*(a^4*d*e^(3*I*d*x + 3*I*c) - a^4*d*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*sqrt(-4*I/(a^5*d^2)) - 3*a^2*e^(2*I*d*x + 2*I*c) + a^2)*e^(-2*I*d*x - 2*I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-41*I*e^(6*I*d*x + 6*I*c) + 48*I*e^(4*I*d*x + 4*I*c) - 8*I*e^(2*I*d*x + 2*I*c) + I))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","B",0
788,0,0,0,1.294271," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, a^{3} \left(\frac{i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} - 1}\right)^{n} e^{\left(6 i \, f x + 6 i \, e\right)}}{e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(8*a^3*((I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) - 1))^n*e^(6*I*f*x + 6*I*e)/(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
789,0,0,0,2.098237," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, a^{2} \left(\frac{i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} - 1}\right)^{n} e^{\left(4 i \, f x + 4 i \, e\right)}}{e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(4*a^2*((I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) - 1))^n*e^(4*I*f*x + 4*I*e)/(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
790,0,0,0,0.896847," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} - 1}\right)^{n} e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*a*((I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) - 1))^n*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
791,0,0,0,0.815042," ","integrate((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} - 1}\right)^{n} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*((I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) - 1))^n*(e^(2*I*f*x + 2*I*e) + 1)*e^(-2*I*f*x - 2*I*e)/a, x)","F",0
792,0,0,0,1.591207," ","integrate((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} - 1}\right)^{n} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*((I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) - 1))^n*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)*e^(-4*I*f*x - 4*I*e)/a^2, x)","F",0
793,0,0,0,2.056072," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \left(\frac{i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} - 1}\right)^{n}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*((I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) - 1))^n, x)","F",0
794,0,0,0,1.628090," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1), x)","F",0
795,0,0,0,0.797359," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1)), x)","F",0
796,0,0,0,0.607320," ","integrate((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(-I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
797,0,0,0,1.961152," ","integrate((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(-(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt((I*e^(2*I*d*x + 2*I*c) + I)/(e^(2*I*d*x + 2*I*c) - 1))*(e^(4*I*d*x + 4*I*c) - 2*e^(2*I*d*x + 2*I*c) + 1)/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
798,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
799,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
802,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
805,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
812,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
813,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
824,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
839,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
843,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
845,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
846,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,0,0,0,1.373380," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \left(d \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*(d*cot(f*x + e))^n, x)","F",0
881,0,0,0,0.827180," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*cot(f*x + e))^n, x)","F",0
882,0,0,0,0.487070," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)} \left(d \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)*(d*cot(f*x + e))^n, x)","F",0
883,0,0,0,0.485243," ","integrate((d*cot(f*x+e))^n/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cot\left(f x + e\right)\right)^{n}}{b \tan\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*cot(f*x + e))^n/(b*tan(f*x + e) + a), x)","F",0
884,0,0,0,0.466574," ","integrate((d*cot(f*x+e))^n/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cot\left(f x + e\right)\right)^{n}}{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*cot(f*x + e))^n/(b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2), x)","F",0
885,0,0,0,0.497743," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cot\left(f x + e\right)\right)^{n} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((d*cot(f*x + e))^n*(b*tan(f*x + e) + a)^m, x)","F",0
886,0,0,0,0.522016," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cot(d*x + c)^(3/2), x)","F",0
887,0,0,0,0.441145," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \sqrt{\cot\left(d x + c\right)}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
888,0,0,0,0.474721," ","integrate((a+b*tan(d*x+c))^n/cot(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{\cot\left(d x + c\right)}}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n/sqrt(cot(d*x + c)), x)","F",0
889,0,0,0,0.504033," ","integrate((a+b*tan(d*x+c))^n/cot(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\cot\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n/cot(d*x + c)^(3/2), x)","F",0
890,1,78,0,0.441288," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{24 i \, a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} + 24 i \, a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{3} c}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(24*I*a^3*c*e^(4*I*f*x + 4*I*e) + 24*I*a^3*c*e^(2*I*f*x + 2*I*e) + 8*I*a^3*c)/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
891,1,50,0,0.474989," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{4 i \, a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a^{2} c}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"(4*I*a^2*c*e^(2*I*f*x + 2*I*e) + 2*I*a^2*c)/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
892,1,19,0,0.433973," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 i \, a c}{f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"2*I*a*c/(f*e^(2*I*f*x + 2*I*e) + f)","C",0
893,1,18,0,0.443522," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{i \, c e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a f}"," ",0,"1/2*I*c*e^(-2*I*f*x - 2*I*e)/(a*f)","A",0
894,1,33,0,0.454931," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(2 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{8 \, a^{2} f}"," ",0,"1/8*(2*I*c*e^(2*I*f*x + 2*I*e) + I*c)*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
895,1,45,0,0.464293," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 i \, c e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{24 \, a^{3} f}"," ",0,"1/24*(3*I*c*e^(4*I*f*x + 4*I*e) + 3*I*c*e^(2*I*f*x + 2*I*e) + I*c)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
896,1,125,0,0.474999," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{80 i \, a^{4} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 80 i \, a^{4} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 40 i \, a^{4} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{4} c^{2}}{5 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/5*(80*I*a^4*c^2*e^(6*I*f*x + 6*I*e) + 80*I*a^4*c^2*e^(4*I*f*x + 4*I*e) + 40*I*a^4*c^2*e^(2*I*f*x + 2*I*e) + 8*I*a^4*c^2)/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","B",0
897,1,96,0,0.421618," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{24 i \, a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 16 i \, a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{3} c^{2}}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(24*I*a^3*c^2*e^(4*I*f*x + 4*I*e) + 16*I*a^3*c^2*e^(2*I*f*x + 2*I*e) + 4*I*a^3*c^2)/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","A",0
898,1,67,0,0.486105," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{12 i \, a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{2} c^{2}}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(12*I*a^2*c^2*e^(2*I*f*x + 2*I*e) + 4*I*a^2*c^2)/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","C",0
899,1,33,0,0.475062," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 i \, a c^{2}}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"2*I*a*c^2/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","A",0
900,1,65,0,0.494370," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(2 \, c^{2} f x e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - i \, c^{2}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a f}"," ",0,"-(2*c^2*f*x*e^(2*I*f*x + 2*I*e) + I*c^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - I*c^2)*e^(-2*I*f*x - 2*I*e)/(a*f)","A",0
901,1,20,0,0.559968," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{i \, c^{2} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2} f}"," ",0,"1/4*I*c^2*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
902,1,37,0,0.515985," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c^{2}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{24 \, a^{3} f}"," ",0,"1/24*(3*I*c^2*e^(2*I*f*x + 2*I*e) + 2*I*c^2)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
903,1,51,0,0.438250," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(6 i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 8 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, c^{2}\right)} e^{\left(-8 i \, f x - 8 i \, e\right)}}{96 \, a^{4} f}"," ",0,"1/96*(6*I*c^2*e^(4*I*f*x + 4*I*e) + 8*I*c^2*e^(2*I*f*x + 2*I*e) + 3*I*c^2)*e^(-8*I*f*x - 8*I*e)/(a^4*f)","A",0
904,1,166,0,0.455507," ","integrate((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{4480 i \, a^{5} c^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + 4480 i \, a^{5} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 2688 i \, a^{5} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 896 i \, a^{5} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 128 i \, a^{5} c^{3}}{105 \, {\left(f e^{\left(14 i \, f x + 14 i \, e\right)} + 7 \, f e^{\left(12 i \, f x + 12 i \, e\right)} + 21 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 35 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 35 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 21 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 7 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/105*(4480*I*a^5*c^3*e^(8*I*f*x + 8*I*e) + 4480*I*a^5*c^3*e^(6*I*f*x + 6*I*e) + 2688*I*a^5*c^3*e^(4*I*f*x + 4*I*e) + 896*I*a^5*c^3*e^(2*I*f*x + 2*I*e) + 128*I*a^5*c^3)/(f*e^(14*I*f*x + 14*I*e) + 7*f*e^(12*I*f*x + 12*I*e) + 21*f*e^(10*I*f*x + 10*I*e) + 35*f*e^(8*I*f*x + 8*I*e) + 35*f*e^(6*I*f*x + 6*I*e) + 21*f*e^(4*I*f*x + 4*I*e) + 7*f*e^(2*I*f*x + 2*I*e) + f)","B",0
905,1,137,0,0.447668," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{320 i \, a^{4} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 240 i \, a^{4} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, a^{4} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{4} c^{3}}{15 \, {\left(f e^{\left(12 i \, f x + 12 i \, e\right)} + 6 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 15 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 20 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 15 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 6 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(320*I*a^4*c^3*e^(6*I*f*x + 6*I*e) + 240*I*a^4*c^3*e^(4*I*f*x + 4*I*e) + 96*I*a^4*c^3*e^(2*I*f*x + 2*I*e) + 16*I*a^4*c^3)/(f*e^(12*I*f*x + 12*I*e) + 6*f*e^(10*I*f*x + 10*I*e) + 15*f*e^(8*I*f*x + 8*I*e) + 20*f*e^(6*I*f*x + 6*I*e) + 15*f*e^(4*I*f*x + 4*I*e) + 6*f*e^(2*I*f*x + 2*I*e) + f)","A",0
906,1,108,0,0.406278," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{160 i \, a^{3} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 80 i \, a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} c^{3}}{15 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(160*I*a^3*c^3*e^(4*I*f*x + 4*I*e) + 80*I*a^3*c^3*e^(2*I*f*x + 2*I*e) + 16*I*a^3*c^3)/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","C",0
907,1,79,0,0.443314," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{16 i \, a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{2} c^{3}}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(16*I*a^2*c^3*e^(2*I*f*x + 2*I*e) + 4*I*a^2*c^3)/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","A",0
908,1,45,0,0.442752," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{8 i \, a c^{3}}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"8/3*I*a*c^3/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
909,1,117,0,0.438244," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{8 \, c^{3} f x e^{\left(4 i \, f x + 4 i \, e\right)} - 2 i \, c^{3} + {\left(8 \, c^{3} f x - 4 i \, c^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(-4 i \, c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 4 i \, c^{3} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"-(8*c^3*f*x*e^(4*I*f*x + 4*I*e) - 2*I*c^3 + (8*c^3*f*x - 4*I*c^3)*e^(2*I*f*x + 2*I*e) - (-4*I*c^3*e^(4*I*f*x + 4*I*e) - 4*I*c^3*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))","A",0
910,1,79,0,0.441453," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, c^{3} f x e^{\left(4 i \, f x + 4 i \, e\right)} + 2 i \, c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 i \, c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c^{3}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{2 \, a^{2} f}"," ",0,"1/2*(4*c^3*f*x*e^(4*I*f*x + 4*I*e) + 2*I*c^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 2*I*c^3*e^(2*I*f*x + 2*I*e) + I*c^3)*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
911,1,20,0,0.429998," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{i \, c^{3} e^{\left(-6 i \, f x - 6 i \, e\right)}}{6 \, a^{3} f}"," ",0,"1/6*I*c^3*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
912,1,37,0,0.418552," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(4 i \, c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, c^{3}\right)} e^{\left(-8 i \, f x - 8 i \, e\right)}}{48 \, a^{4} f}"," ",0,"1/48*(4*I*c^3*e^(2*I*f*x + 2*I*e) + 3*I*c^3)*e^(-8*I*f*x - 8*I*e)/(a^4*f)","A",0
913,1,51,0,0.439483," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(10 i \, c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 15 i \, c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, c^{3}\right)} e^{\left(-10 i \, f x - 10 i \, e\right)}}{240 \, a^{5} f}"," ",0,"1/240*(10*I*c^3*e^(4*I*f*x + 4*I*e) + 15*I*c^3*e^(2*I*f*x + 2*I*e) + 6*I*c^3)*e^(-10*I*f*x - 10*I*e)/(a^5*f)","A",0
914,1,178,0,0.436151," ","integrate((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{2240 i \, a^{5} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + 1792 i \, a^{5} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 896 i \, a^{5} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 256 i \, a^{5} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 32 i \, a^{5} c^{4}}{35 \, {\left(f e^{\left(16 i \, f x + 16 i \, e\right)} + 8 \, f e^{\left(14 i \, f x + 14 i \, e\right)} + 28 \, f e^{\left(12 i \, f x + 12 i \, e\right)} + 56 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 70 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 56 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 28 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 8 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/35*(2240*I*a^5*c^4*e^(8*I*f*x + 8*I*e) + 1792*I*a^5*c^4*e^(6*I*f*x + 6*I*e) + 896*I*a^5*c^4*e^(4*I*f*x + 4*I*e) + 256*I*a^5*c^4*e^(2*I*f*x + 2*I*e) + 32*I*a^5*c^4)/(f*e^(16*I*f*x + 16*I*e) + 8*f*e^(14*I*f*x + 14*I*e) + 28*f*e^(12*I*f*x + 12*I*e) + 56*f*e^(10*I*f*x + 10*I*e) + 70*f*e^(8*I*f*x + 8*I*e) + 56*f*e^(6*I*f*x + 6*I*e) + 28*f*e^(4*I*f*x + 4*I*e) + 8*f*e^(2*I*f*x + 2*I*e) + f)","A",0
915,1,149,0,0.413962," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{1120 i \, a^{4} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 672 i \, a^{4} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 224 i \, a^{4} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 32 i \, a^{4} c^{4}}{35 \, {\left(f e^{\left(14 i \, f x + 14 i \, e\right)} + 7 \, f e^{\left(12 i \, f x + 12 i \, e\right)} + 21 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 35 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 35 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 21 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 7 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/35*(1120*I*a^4*c^4*e^(6*I*f*x + 6*I*e) + 672*I*a^4*c^4*e^(4*I*f*x + 4*I*e) + 224*I*a^4*c^4*e^(2*I*f*x + 2*I*e) + 32*I*a^4*c^4)/(f*e^(14*I*f*x + 14*I*e) + 7*f*e^(12*I*f*x + 12*I*e) + 21*f*e^(10*I*f*x + 10*I*e) + 35*f*e^(8*I*f*x + 8*I*e) + 35*f*e^(6*I*f*x + 6*I*e) + 21*f*e^(4*I*f*x + 4*I*e) + 7*f*e^(2*I*f*x + 2*I*e) + f)","C",0
916,1,120,0,0.440771," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{240 i \, a^{3} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, a^{3} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} c^{4}}{15 \, {\left(f e^{\left(12 i \, f x + 12 i \, e\right)} + 6 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 15 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 20 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 15 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 6 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(240*I*a^3*c^4*e^(4*I*f*x + 4*I*e) + 96*I*a^3*c^4*e^(2*I*f*x + 2*I*e) + 16*I*a^3*c^4)/(f*e^(12*I*f*x + 12*I*e) + 6*f*e^(10*I*f*x + 10*I*e) + 15*f*e^(8*I*f*x + 8*I*e) + 20*f*e^(6*I*f*x + 6*I*e) + 15*f*e^(4*I*f*x + 4*I*e) + 6*f*e^(2*I*f*x + 2*I*e) + f)","A",0
917,1,91,0,0.481052," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{40 i \, a^{2} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} c^{4}}{5 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/5*(40*I*a^2*c^4*e^(2*I*f*x + 2*I*e) + 8*I*a^2*c^4)/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","A",0
918,1,57,0,0.422182," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{4 i \, a c^{4}}{f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"4*I*a*c^4/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
919,1,167,0,0.510853," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{24 \, c^{4} f x e^{\left(6 i \, f x + 6 i \, e\right)} - 4 i \, c^{4} + {\left(48 \, c^{4} f x - 12 i \, c^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 \, c^{4} f x - 18 i \, c^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(-12 i \, c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} - 24 i \, c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} - 12 i \, c^{4} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{a f e^{\left(6 i \, f x + 6 i \, e\right)} + 2 \, a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"-(24*c^4*f*x*e^(6*I*f*x + 6*I*e) - 4*I*c^4 + (48*c^4*f*x - 12*I*c^4)*e^(4*I*f*x + 4*I*e) + (24*c^4*f*x - 18*I*c^4)*e^(2*I*f*x + 2*I*e) - (-12*I*c^4*e^(6*I*f*x + 6*I*e) - 24*I*c^4*e^(4*I*f*x + 4*I*e) - 12*I*c^4*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a*f*e^(6*I*f*x + 6*I*e) + 2*a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))","A",0
920,1,133,0,0.444221," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{12 \, c^{4} f x e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c^{4} + {\left(12 \, c^{4} f x - 6 i \, c^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 i \, c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 6 i \, c^{4} e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{a^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)}}"," ",0,"(12*c^4*f*x*e^(6*I*f*x + 6*I*e) - 3*I*c^4*e^(2*I*f*x + 2*I*e) + I*c^4 + (12*c^4*f*x - 6*I*c^4)*e^(4*I*f*x + 4*I*e) + (6*I*c^4*e^(6*I*f*x + 6*I*e) + 6*I*c^4*e^(4*I*f*x + 4*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a^2*f*e^(6*I*f*x + 6*I*e) + a^2*f*e^(4*I*f*x + 4*I*e))","A",0
921,1,93,0,0.445102," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(12 \, c^{4} f x e^{\left(6 i \, f x + 6 i \, e\right)} + 6 i \, c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 6 i \, c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i \, c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c^{4}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{6 \, a^{3} f}"," ",0,"-1/6*(12*c^4*f*x*e^(6*I*f*x + 6*I*e) + 6*I*c^4*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 6*I*c^4*e^(4*I*f*x + 4*I*e) + 3*I*c^4*e^(2*I*f*x + 2*I*e) - 2*I*c^4)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
922,1,20,0,0.486789," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{i \, c^{4} e^{\left(-8 i \, f x - 8 i \, e\right)}}{8 \, a^{4} f}"," ",0,"1/8*I*c^4*e^(-8*I*f*x - 8*I*e)/(a^4*f)","A",0
923,1,37,0,0.426943," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(5 i \, c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c^{4}\right)} e^{\left(-10 i \, f x - 10 i \, e\right)}}{80 \, a^{5} f}"," ",0,"1/80*(5*I*c^4*e^(2*I*f*x + 2*I*e) + 4*I*c^4)*e^(-10*I*f*x - 10*I*e)/(a^5*f)","A",0
924,1,127,0,0.476491," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{-4 i \, a^{4} e^{\left(6 i \, f x + 6 i \, e\right)} - 8 i \, a^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 8 i \, a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 10 i \, a^{4} + {\left(12 i \, a^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 24 i \, a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 12 i \, a^{4}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{c f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f}"," ",0,"(-4*I*a^4*e^(6*I*f*x + 6*I*e) - 8*I*a^4*e^(4*I*f*x + 4*I*e) + 8*I*a^4*e^(2*I*f*x + 2*I*e) + 10*I*a^4 + (12*I*a^4*e^(4*I*f*x + 4*I*e) + 24*I*a^4*e^(2*I*f*x + 2*I*e) + 12*I*a^4)*log(e^(2*I*f*x + 2*I*e) + 1))/(c*f*e^(4*I*f*x + 4*I*e) + 2*c*f*e^(2*I*f*x + 2*I*e) + c*f)","A",0
925,1,86,0,0.479169," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{-2 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 2 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a^{3} + {\left(4 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{3}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f}"," ",0,"(-2*I*a^3*e^(4*I*f*x + 4*I*e) - 2*I*a^3*e^(2*I*f*x + 2*I*e) + 2*I*a^3 + (4*I*a^3*e^(2*I*f*x + 2*I*e) + 4*I*a^3)*log(e^(2*I*f*x + 2*I*e) + 1))/(c*f*e^(2*I*f*x + 2*I*e) + c*f)","A",0
926,1,39,0,0.477685," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{-i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, a^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{c f}"," ",0,"(-I*a^2*e^(2*I*f*x + 2*I*e) + I*a^2*log(e^(2*I*f*x + 2*I*e) + 1))/(c*f)","A",0
927,1,18,0,0.519818," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{i \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{2 \, c f}"," ",0,"-1/2*I*a*e^(2*I*f*x + 2*I*e)/(c*f)","A",0
928,1,46,0,0.520153," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(4 \, f x e^{\left(2 i \, f x + 2 i \, e\right)} - i \, e^{\left(4 i \, f x + 4 i \, e\right)} + i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a c f}"," ",0,"1/8*(4*f*x*e^(2*I*f*x + 2*I*e) - I*e^(4*I*f*x + 4*I*e) + I)*e^(-2*I*f*x - 2*I*e)/(a*c*f)","C",0
929,1,57,0,0.525162," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(12 \, f x e^{\left(4 i \, f x + 4 i \, e\right)} - 2 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 6 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{32 \, a^{2} c f}"," ",0,"1/32*(12*f*x*e^(4*I*f*x + 4*I*e) - 2*I*e^(6*I*f*x + 6*I*e) + 6*I*e^(2*I*f*x + 2*I*e) + I)*e^(-4*I*f*x - 4*I*e)/(a^2*c*f)","A",0
930,1,68,0,0.483845," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(24 \, f x e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 18 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 6 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} c f}"," ",0,"1/96*(24*f*x*e^(6*I*f*x + 6*I*e) - 3*I*e^(8*I*f*x + 8*I*e) + 18*I*e^(4*I*f*x + 4*I*e) + 6*I*e^(2*I*f*x + 2*I*e) + I)*e^(-6*I*f*x - 6*I*e)/(a^3*c*f)","A",0
931,1,104,0,0.505850," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-i \, a^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 3 i \, a^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 4 i \, a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a^{4} + {\left(-6 i \, a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} - 6 i \, a^{4}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f}"," ",0,"(-I*a^4*e^(6*I*f*x + 6*I*e) + 3*I*a^4*e^(4*I*f*x + 4*I*e) + 4*I*a^4*e^(2*I*f*x + 2*I*e) - 2*I*a^4 + (-6*I*a^4*e^(2*I*f*x + 2*I*e) - 6*I*a^4)*log(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f*e^(2*I*f*x + 2*I*e) + c^2*f)","A",0
932,1,54,0,0.450695," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{2 \, c^{2} f}"," ",0,"1/2*(-I*a^3*e^(4*I*f*x + 4*I*e) + 2*I*a^3*e^(2*I*f*x + 2*I*e) - 2*I*a^3*log(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","A",0
933,1,20,0,0.426778," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{4 \, c^{2} f}"," ",0,"-1/4*I*a^2*e^(4*I*f*x + 4*I*e)/(c^2*f)","A",0
934,1,33,0,0.434972," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 2 i \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{8 \, c^{2} f}"," ",0,"1/8*(-I*a*e^(4*I*f*x + 4*I*e) - 2*I*a*e^(2*I*f*x + 2*I*e))/(c^2*f)","A",0
935,1,57,0,0.467633," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(12 \, f x e^{\left(2 i \, f x + 2 i \, e\right)} - i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 6 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 2 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{32 \, a c^{2} f}"," ",0,"1/32*(12*f*x*e^(2*I*f*x + 2*I*e) - I*e^(6*I*f*x + 6*I*e) - 6*I*e^(4*I*f*x + 4*I*e) + 2*I)*e^(-2*I*f*x - 2*I*e)/(a*c^2*f)","A",0
936,1,68,0,0.457884," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, f x e^{\left(4 i \, f x + 4 i \, e\right)} - i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 8 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 8 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{64 \, a^{2} c^{2} f}"," ",0,"1/64*(24*f*x*e^(4*I*f*x + 4*I*e) - I*e^(8*I*f*x + 8*I*e) - 8*I*e^(6*I*f*x + 6*I*e) + 8*I*e^(2*I*f*x + 2*I*e) + I)*e^(-4*I*f*x - 4*I*e)/(a^2*c^2*f)","C",0
937,1,79,0,0.465544," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(120 \, f x e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 30 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 60 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 15 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{384 \, a^{3} c^{2} f}"," ",0,"1/384*(120*f*x*e^(6*I*f*x + 6*I*e) - 3*I*e^(10*I*f*x + 10*I*e) - 30*I*e^(8*I*f*x + 8*I*e) + 60*I*e^(4*I*f*x + 4*I*e) + 15*I*e^(2*I*f*x + 2*I*e) + 2*I)*e^(-6*I*f*x - 6*I*e)/(a^3*c^2*f)","A",0
938,1,162,0,0.530645," ","integrate((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-4 i \, a^{6} e^{\left(10 i \, f x + 10 i \, e\right)} + 10 i \, a^{6} e^{\left(8 i \, f x + 8 i \, e\right)} - 40 i \, a^{6} e^{\left(6 i \, f x + 6 i \, e\right)} - 126 i \, a^{6} e^{\left(4 i \, f x + 4 i \, e\right)} - 12 i \, a^{6} e^{\left(2 i \, f x + 2 i \, e\right)} + 54 i \, a^{6} + {\left(120 i \, a^{6} e^{\left(4 i \, f x + 4 i \, e\right)} + 240 i \, a^{6} e^{\left(2 i \, f x + 2 i \, e\right)} + 120 i \, a^{6}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(c^{3} f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{3} f\right)}}"," ",0,"1/3*(-4*I*a^6*e^(10*I*f*x + 10*I*e) + 10*I*a^6*e^(8*I*f*x + 8*I*e) - 40*I*a^6*e^(6*I*f*x + 6*I*e) - 126*I*a^6*e^(4*I*f*x + 4*I*e) - 12*I*a^6*e^(2*I*f*x + 2*I*e) + 54*I*a^6 + (120*I*a^6*e^(4*I*f*x + 4*I*e) + 240*I*a^6*e^(2*I*f*x + 2*I*e) + 120*I*a^6)*log(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f*e^(4*I*f*x + 4*I*e) + 2*c^3*f*e^(2*I*f*x + 2*I*e) + c^3*f)","A",0
939,1,119,0,0.526903," ","integrate((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-2 i \, a^{5} e^{\left(8 i \, f x + 8 i \, e\right)} + 4 i \, a^{5} e^{\left(6 i \, f x + 6 i \, e\right)} - 12 i \, a^{5} e^{\left(4 i \, f x + 4 i \, e\right)} - 18 i \, a^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, a^{5} + {\left(24 i \, a^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + 24 i \, a^{5}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{3} f\right)}}"," ",0,"1/3*(-2*I*a^5*e^(8*I*f*x + 8*I*e) + 4*I*a^5*e^(6*I*f*x + 6*I*e) - 12*I*a^5*e^(4*I*f*x + 4*I*e) - 18*I*a^5*e^(2*I*f*x + 2*I*e) + 6*I*a^5 + (24*I*a^5*e^(2*I*f*x + 2*I*e) + 24*I*a^5)*log(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f*e^(2*I*f*x + 2*I*e) + c^3*f)","A",0
940,1,68,0,0.455717," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-2 i \, a^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 3 i \, a^{4} e^{\left(4 i \, f x + 4 i \, e\right)} - 6 i \, a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, a^{4} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{6 \, c^{3} f}"," ",0,"1/6*(-2*I*a^4*e^(6*I*f*x + 6*I*e) + 3*I*a^4*e^(4*I*f*x + 4*I*e) - 6*I*a^4*e^(2*I*f*x + 2*I*e) + 6*I*a^4*log(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
941,1,20,0,0.488865," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{i \, a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{6 \, c^{3} f}"," ",0,"-1/6*I*a^3*e^(6*I*f*x + 6*I*e)/(c^3*f)","A",0
942,1,37,0,0.482483," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-2 i \, a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{24 \, c^{3} f}"," ",0,"1/24*(-2*I*a^2*e^(6*I*f*x + 6*I*e) - 3*I*a^2*e^(4*I*f*x + 4*I*e))/(c^3*f)","A",0
943,1,45,0,0.413216," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-i \, a e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 3 i \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{24 \, c^{3} f}"," ",0,"1/24*(-I*a*e^(6*I*f*x + 6*I*e) - 3*I*a*e^(4*I*f*x + 4*I*e) - 3*I*a*e^(2*I*f*x + 2*I*e))/(c^3*f)","B",0
944,1,68,0,0.484136," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(24 \, f x e^{\left(2 i \, f x + 2 i \, e\right)} - i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 6 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 18 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{96 \, a c^{3} f}"," ",0,"1/96*(24*f*x*e^(2*I*f*x + 2*I*e) - I*e^(8*I*f*x + 8*I*e) - 6*I*e^(6*I*f*x + 6*I*e) - 18*I*e^(4*I*f*x + 4*I*e) + 3*I)*e^(-2*I*f*x - 2*I*e)/(a*c^3*f)","A",0
945,1,79,0,0.417783," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(120 \, f x e^{\left(4 i \, f x + 4 i \, e\right)} - 2 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 15 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 60 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 30 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{384 \, a^{2} c^{3} f}"," ",0,"1/384*(120*f*x*e^(4*I*f*x + 4*I*e) - 2*I*e^(10*I*f*x + 10*I*e) - 15*I*e^(8*I*f*x + 8*I*e) - 60*I*e^(6*I*f*x + 6*I*e) + 30*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(-4*I*f*x - 4*I*e)/(a^2*c^3*f)","A",0
946,1,90,0,0.432999," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(120 \, f x e^{\left(6 i \, f x + 6 i \, e\right)} - i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 9 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 45 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 45 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 9 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{384 \, a^{3} c^{3} f}"," ",0,"1/384*(120*f*x*e^(6*I*f*x + 6*I*e) - I*e^(12*I*f*x + 12*I*e) - 9*I*e^(10*I*f*x + 10*I*e) - 45*I*e^(8*I*f*x + 8*I*e) + 45*I*e^(4*I*f*x + 4*I*e) + 9*I*e^(2*I*f*x + 2*I*e) + I)*e^(-6*I*f*x - 6*I*e)/(a^3*c^3*f)","C",0
947,1,133,0,0.462513," ","integrate((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{-3 i \, a^{6} e^{\left(10 i \, f x + 10 i \, e\right)} + 5 i \, a^{6} e^{\left(8 i \, f x + 8 i \, e\right)} - 10 i \, a^{6} e^{\left(6 i \, f x + 6 i \, e\right)} + 30 i \, a^{6} e^{\left(4 i \, f x + 4 i \, e\right)} + 48 i \, a^{6} e^{\left(2 i \, f x + 2 i \, e\right)} - 12 i \, a^{6} + {\left(-60 i \, a^{6} e^{\left(2 i \, f x + 2 i \, e\right)} - 60 i \, a^{6}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{6 \, {\left(c^{4} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{4} f\right)}}"," ",0,"1/6*(-3*I*a^6*e^(10*I*f*x + 10*I*e) + 5*I*a^6*e^(8*I*f*x + 8*I*e) - 10*I*a^6*e^(6*I*f*x + 6*I*e) + 30*I*a^6*e^(4*I*f*x + 4*I*e) + 48*I*a^6*e^(2*I*f*x + 2*I*e) - 12*I*a^6 + (-60*I*a^6*e^(2*I*f*x + 2*I*e) - 60*I*a^6)*log(e^(2*I*f*x + 2*I*e) + 1))/(c^4*f*e^(2*I*f*x + 2*I*e) + c^4*f)","A",0
948,1,82,0,0.639528," ","integrate((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{-3 i \, a^{5} e^{\left(8 i \, f x + 8 i \, e\right)} + 4 i \, a^{5} e^{\left(6 i \, f x + 6 i \, e\right)} - 6 i \, a^{5} e^{\left(4 i \, f x + 4 i \, e\right)} + 12 i \, a^{5} e^{\left(2 i \, f x + 2 i \, e\right)} - 12 i \, a^{5} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{12 \, c^{4} f}"," ",0,"1/12*(-3*I*a^5*e^(8*I*f*x + 8*I*e) + 4*I*a^5*e^(6*I*f*x + 6*I*e) - 6*I*a^5*e^(4*I*f*x + 4*I*e) + 12*I*a^5*e^(2*I*f*x + 2*I*e) - 12*I*a^5*log(e^(2*I*f*x + 2*I*e) + 1))/(c^4*f)","A",0
949,1,20,0,0.535081," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","-\frac{i \, a^{4} e^{\left(8 i \, f x + 8 i \, e\right)}}{8 \, c^{4} f}"," ",0,"-1/8*I*a^4*e^(8*I*f*x + 8*I*e)/(c^4*f)","A",0
950,1,37,0,0.434152," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{-3 i \, a^{3} e^{\left(8 i \, f x + 8 i \, e\right)} - 4 i \, a^{3} e^{\left(6 i \, f x + 6 i \, e\right)}}{48 \, c^{4} f}"," ",0,"1/48*(-3*I*a^3*e^(8*I*f*x + 8*I*e) - 4*I*a^3*e^(6*I*f*x + 6*I*e))/(c^4*f)","A",0
951,1,51,0,0.418143," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{-3 i \, a^{2} e^{\left(8 i \, f x + 8 i \, e\right)} - 8 i \, a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 6 i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)}}{96 \, c^{4} f}"," ",0,"1/96*(-3*I*a^2*e^(8*I*f*x + 8*I*e) - 8*I*a^2*e^(6*I*f*x + 6*I*e) - 6*I*a^2*e^(4*I*f*x + 4*I*e))/(c^4*f)","A",0
952,1,57,0,0.588218," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{-i \, a e^{\left(8 i \, f x + 8 i \, e\right)} - 4 i \, a e^{\left(6 i \, f x + 6 i \, e\right)} - 6 i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 4 i \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{64 \, c^{4} f}"," ",0,"1/64*(-I*a*e^(8*I*f*x + 8*I*e) - 4*I*a*e^(6*I*f*x + 6*I*e) - 6*I*a*e^(4*I*f*x + 4*I*e) - 4*I*a*e^(2*I*f*x + 2*I*e))/(c^4*f)","B",0
953,1,79,0,0.833226," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(120 \, f x e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 20 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 60 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 120 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 12 i\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{768 \, a c^{4} f}"," ",0,"1/768*(120*f*x*e^(2*I*f*x + 2*I*e) - 3*I*e^(10*I*f*x + 10*I*e) - 20*I*e^(8*I*f*x + 8*I*e) - 60*I*e^(6*I*f*x + 6*I*e) - 120*I*e^(4*I*f*x + 4*I*e) + 12*I)*e^(-2*I*f*x - 2*I*e)/(a*c^4*f)","A",0
954,1,90,0,0.516112," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(120 \, f x e^{\left(4 i \, f x + 4 i \, e\right)} - i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 8 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 30 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 80 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 24 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{512 \, a^{2} c^{4} f}"," ",0,"1/512*(120*f*x*e^(4*I*f*x + 4*I*e) - I*e^(12*I*f*x + 12*I*e) - 8*I*e^(10*I*f*x + 10*I*e) - 30*I*e^(8*I*f*x + 8*I*e) - 80*I*e^(6*I*f*x + 6*I*e) + 24*I*e^(2*I*f*x + 2*I*e) + 2*I)*e^(-4*I*f*x - 4*I*e)/(a^2*c^4*f)","A",0
955,1,101,0,0.413116," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(840 \, f x e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, e^{\left(14 i \, f x + 14 i \, e\right)} - 28 i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 126 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 420 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 252 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 42 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{3072 \, a^{3} c^{4} f}"," ",0,"1/3072*(840*f*x*e^(6*I*f*x + 6*I*e) - 3*I*e^(14*I*f*x + 14*I*e) - 28*I*e^(12*I*f*x + 12*I*e) - 126*I*e^(10*I*f*x + 10*I*e) - 420*I*e^(8*I*f*x + 8*I*e) + 252*I*e^(4*I*f*x + 4*I*e) + 42*I*e^(2*I*f*x + 2*I*e) + 4*I)*e^(-6*I*f*x - 6*I*e)/(a^3*c^4*f)","A",0
956,1,83,0,0.436921," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(120 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 160 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 64 i \, a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{15 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*sqrt(2)*(120*I*a^3*e^(4*I*f*x + 4*I*e) + 160*I*a^3*e^(2*I*f*x + 2*I*e) + 64*I*a^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","A",0
957,1,57,0,0.440527," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(12 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*sqrt(2)*(12*I*a^2*e^(2*I*f*x + 2*I*e) + 8*I*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(2*I*f*x + 2*I*e) + f)","A",0
958,1,26,0,0.456330," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} a \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{f}"," ",0,"2*I*sqrt(2)*a*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/f","A",0
959,1,250,0,0.468688," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(\sqrt{\frac{1}{2}} a f \sqrt{-\frac{c}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c}{a^{2} f^{2}}} + i \, c\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) - \sqrt{\frac{1}{2}} a f \sqrt{-\frac{c}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c}{a^{2} f^{2}}} - i \, c\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*(sqrt(1/2)*a*f*sqrt(-c/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((sqrt(2)*sqrt(1/2)*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c/(a^2*f^2)) + I*c)*e^(-I*f*x - I*e)/(a*f)) - sqrt(1/2)*a*f*sqrt(-c/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(-(sqrt(2)*sqrt(1/2)*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c/(a^2*f^2)) - I*c)*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(I*e^(2*I*f*x + 2*I*e) + I))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
960,1,275,0,0.476173," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{3 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c}{a^{4} f^{2}}} + i \, c\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{2} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{3 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c}{a^{4} f^{2}}} - i \, c\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{2} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(5 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 7 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{32 \, a^{2} f}"," ",0,"1/32*(3*sqrt(1/2)*a^2*f*sqrt(-c/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(3/8*(sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c/(a^4*f^2)) + I*c)*e^(-I*f*x - I*e)/(a^2*f)) - 3*sqrt(1/2)*a^2*f*sqrt(-c/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(-3/8*(sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c/(a^4*f^2)) - I*c)*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(5*I*e^(4*I*f*x + 4*I*e) + 7*I*e^(2*I*f*x + 2*I*e) + 2*I))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
961,1,286,0,0.489289," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{5 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c}{a^{6} f^{2}}} + i \, c\right)} e^{\left(-i \, f x - i \, e\right)}}{32 \, a^{3} f}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{5 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c}{a^{6} f^{2}}} - i \, c\right)} e^{\left(-i \, f x - i \, e\right)}}{32 \, a^{3} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(33 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 59 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 34 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{384 \, a^{3} f}"," ",0,"1/384*(15*sqrt(1/2)*a^3*f*sqrt(-c/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(5/32*(sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c/(a^6*f^2)) + I*c)*e^(-I*f*x - I*e)/(a^3*f)) - 15*sqrt(1/2)*a^3*f*sqrt(-c/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(-5/32*(sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c/(a^6*f^2)) - I*c)*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(33*I*e^(6*I*f*x + 6*I*e) + 59*I*e^(4*I*f*x + 4*I*e) + 34*I*e^(2*I*f*x + 2*I*e) + 8*I))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
962,1,98,0,0.584385," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(560 i \, a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} + 448 i \, a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + 128 i \, a^{3} c\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{105 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/105*sqrt(2)*(560*I*a^3*c*e^(4*I*f*x + 4*I*e) + 448*I*a^3*c*e^(2*I*f*x + 2*I*e) + 128*I*a^3*c)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","A",0
963,1,71,0,0.451973," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(40 i \, a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{2} c\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{15 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*sqrt(2)*(40*I*a^2*c*e^(2*I*f*x + 2*I*e) + 16*I*a^2*c)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","A",0
964,1,39,0,0.415450," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{4 i \, \sqrt{2} a c \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"4/3*I*sqrt(2)*a*c*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
965,1,254,0,0.505178," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} a f \sqrt{-\frac{c^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-2 i \, c^{2} + 2 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3}}{a^{2} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) - \sqrt{2} a f \sqrt{-\frac{c^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-2 i \, c^{2} - 2 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3}}{a^{2} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) + \sqrt{2} {\left(2 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*(sqrt(2)*a*f*sqrt(-c^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((-2*I*c^2 + 2*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^3/(a^2*f^2)))*e^(-I*f*x - I*e)/(a*f)) - sqrt(2)*a*f*sqrt(-c^3/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((-2*I*c^2 - 2*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^3/(a^2*f^2)))*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*(2*I*c*e^(2*I*f*x + 2*I*e) + 2*I*c)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
966,1,291,0,0.618093," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(\sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{3}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3}}{a^{4} f^{2}}} + i \, c^{2}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2} f}\right) - \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{3}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3}}{a^{4} f^{2}}} - i \, c^{2}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2} f}\right) - \sqrt{2} {\left(i \, c e^{\left(4 i \, f x + 4 i \, e\right)} + 3 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"-1/16*(sqrt(1/2)*a^2*f*sqrt(-c^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/4*(sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^3/(a^4*f^2)) + I*c^2)*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(1/2)*a^2*f*sqrt(-c^3/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*(sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^3/(a^4*f^2)) - I*c^2)*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(2)*(I*c*e^(4*I*f*x + 4*I*e) + 3*I*c*e^(2*I*f*x + 2*I*e) + 2*I*c)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
967,1,304,0,0.504085," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{3}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3}}{a^{6} f^{2}}} + i \, c^{2}\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a^{3} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{3}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3}}{a^{6} f^{2}}} - i \, c^{2}\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a^{3} f}\right) - \sqrt{2} {\left(3 i \, c e^{\left(6 i \, f x + 6 i \, e\right)} + 17 i \, c e^{\left(4 i \, f x + 4 i \, e\right)} + 22 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, c\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{192 \, a^{3} f}"," ",0,"-1/192*(3*sqrt(1/2)*a^3*f*sqrt(-c^3/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/16*(sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^3/(a^6*f^2)) + I*c^2)*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*f*sqrt(-c^3/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16*(sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^3/(a^6*f^2)) - I*c^2)*e^(-I*f*x - I*e)/(a^3*f)) - sqrt(2)*(3*I*c*e^(6*I*f*x + 6*I*e) + 17*I*c*e^(4*I*f*x + 4*I*e) + 22*I*c*e^(2*I*f*x + 2*I*e) + 8*I*c)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
968,1,116,0,0.566858," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(2016 i \, a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 1152 i \, a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 256 i \, a^{3} c^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{315 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/315*sqrt(2)*(2016*I*a^3*c^2*e^(4*I*f*x + 4*I*e) + 1152*I*a^3*c^2*e^(2*I*f*x + 2*I*e) + 256*I*a^3*c^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","A",0
969,1,87,0,0.658875," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(112 i \, a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 32 i \, a^{2} c^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{35 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/35*sqrt(2)*(112*I*a^2*c^2*e^(2*I*f*x + 2*I*e) + 32*I*a^2*c^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","A",0
970,1,53,0,0.519893," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{8 i \, \sqrt{2} a c^{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{5 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"8/5*I*sqrt(2)*a*c^2*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
971,1,259,0,0.629932," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(6 \, \sqrt{2} a \sqrt{-\frac{c^{5}}{a^{2} f^{2}}} f e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-12 i \, c^{3} + 12 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{c^{5}}{a^{2} f^{2}}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) - 6 \, \sqrt{2} a \sqrt{-\frac{c^{5}}{a^{2} f^{2}}} f e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(-12 i \, c^{3} - 12 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{-\frac{c^{5}}{a^{2} f^{2}}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}\right) + \sqrt{2} {\left(12 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*(6*sqrt(2)*a*sqrt(-c^5/(a^2*f^2))*f*e^(2*I*f*x + 2*I*e)*log((-12*I*c^3 + 12*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-c^5/(a^2*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)) - 6*sqrt(2)*a*sqrt(-c^5/(a^2*f^2))*f*e^(2*I*f*x + 2*I*e)*log((-12*I*c^3 - 12*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(-c^5/(a^2*f^2))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*(12*I*c^2*e^(2*I*f*x + 2*I*e) + 4*I*c^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
972,1,299,0,0.460678," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{3 \, {\left(-i \, c^{3} + \sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5}}{a^{4} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a^{2} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{3 \, {\left(-i \, c^{3} - \sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5}}{a^{4} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a^{2} f}\right) - \sqrt{2} {\left(-3 i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{8 \, a^{2} f}"," ",0,"-1/8*(3*sqrt(1/2)*a^2*f*sqrt(-c^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(-3/2*(-I*c^3 + sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^5/(a^4*f^2)))*e^(-I*f*x - I*e)/(a^2*f)) - 3*sqrt(1/2)*a^2*f*sqrt(-c^5/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(-3/2*(-I*c^3 - sqrt(2)*sqrt(1/2)*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^5/(a^4*f^2)))*e^(-I*f*x - I*e)/(a^2*f)) - sqrt(2)*(-3*I*c^2*e^(4*I*f*x + 4*I*e) - I*c^2*e^(2*I*f*x + 2*I*e) + 2*I*c^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
973,1,312,0,0.845677," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{5}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(i \, c^{3} + \sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5}}{a^{6} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{3} f}\right) - 3 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{5}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(i \, c^{3} - \sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5}}{a^{6} f^{2}}}\right)} e^{\left(-i \, f x - i \, e\right)}}{8 \, a^{3} f}\right) + \sqrt{2} {\left(-3 i \, c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 10 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, c^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} f}"," ",0,"1/96*(3*sqrt(1/2)*a^3*f*sqrt(-c^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(I*c^3 + sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^5/(a^6*f^2)))*e^(-I*f*x - I*e)/(a^3*f)) - 3*sqrt(1/2)*a^3*f*sqrt(-c^5/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(I*c^3 - sqrt(2)*sqrt(1/2)*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-c^5/(a^6*f^2)))*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*(-3*I*c^2*e^(6*I*f*x + 6*I*e) - I*c^2*e^(4*I*f*x + 4*I*e) + 10*I*c^2*e^(2*I*f*x + 2*I*e) + 8*I*c^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
974,1,74,0,0.528084," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-12 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 48 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 32 i \, a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)}}"," ",0,"1/3*sqrt(2)*(-12*I*a^3*e^(4*I*f*x + 4*I*e) - 48*I*a^3*e^(2*I*f*x + 2*I*e) - 32*I*a^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c*f*e^(2*I*f*x + 2*I*e) + c*f)","A",0
975,1,47,0,0.494890," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-2 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c f}"," ",0,"sqrt(2)*(-2*I*a^2*e^(2*I*f*x + 2*I*e) - 4*I*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c*f)","A",0
976,1,43,0,0.442102," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - i \, a\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c f}"," ",0,"sqrt(2)*(-I*a*e^(2*I*f*x + 2*I*e) - I*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c*f)","B",0
977,1,272,0,0.464974," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(3 i \, \sqrt{\frac{1}{2}} a c f \sqrt{\frac{1}{a^{2} c f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(6 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i \, a f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{2} c f^{2}}} + 6 i\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a f}\right) - 3 i \, \sqrt{\frac{1}{2}} a c f \sqrt{\frac{1}{a^{2} c f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-6 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 6 i \, a f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{2} c f^{2}}} + 6 i\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-2 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a c f}"," ",0,"1/8*(3*I*sqrt(1/2)*a*c*f*sqrt(1/(a^2*c*f^2))*e^(2*I*f*x + 2*I*e)*log(1/4*(sqrt(2)*sqrt(1/2)*(6*I*a*f*e^(2*I*f*x + 2*I*e) + 6*I*a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^2*c*f^2)) + 6*I)*e^(-I*f*x - I*e)/(a*f)) - 3*I*sqrt(1/2)*a*c*f*sqrt(1/(a^2*c*f^2))*e^(2*I*f*x + 2*I*e)*log(1/4*(sqrt(2)*sqrt(1/2)*(-6*I*a*f*e^(2*I*f*x + 2*I*e) - 6*I*a*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^2*c*f^2)) + 6*I)*e^(-I*f*x - I*e)/(a*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-2*I*e^(4*I*f*x + 4*I*e) - I*e^(2*I*f*x + 2*I*e) + I))*e^(-2*I*f*x - 2*I*e)/(a*c*f)","B",0
978,1,295,0,0.483167," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(15 i \, \sqrt{\frac{1}{2}} a^{2} c f \sqrt{\frac{1}{a^{4} c f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(240 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 240 i \, a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{4} c f^{2}}} + 240 i\right)} e^{\left(-i \, f x - i \, e\right)}}{256 \, a^{2} f}\right) - 15 i \, \sqrt{\frac{1}{2}} a^{2} c f \sqrt{\frac{1}{a^{4} c f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-240 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 240 i \, a^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{4} c f^{2}}} + 240 i\right)} e^{\left(-i \, f x - i \, e\right)}}{256 \, a^{2} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-8 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 11 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{64 \, a^{2} c f}"," ",0,"1/64*(15*I*sqrt(1/2)*a^2*c*f*sqrt(1/(a^4*c*f^2))*e^(4*I*f*x + 4*I*e)*log(1/256*(sqrt(2)*sqrt(1/2)*(240*I*a^2*f*e^(2*I*f*x + 2*I*e) + 240*I*a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^4*c*f^2)) + 240*I)*e^(-I*f*x - I*e)/(a^2*f)) - 15*I*sqrt(1/2)*a^2*c*f*sqrt(1/(a^4*c*f^2))*e^(4*I*f*x + 4*I*e)*log(1/256*(sqrt(2)*sqrt(1/2)*(-240*I*a^2*f*e^(2*I*f*x + 2*I*e) - 240*I*a^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^4*c*f^2)) + 240*I)*e^(-I*f*x - I*e)/(a^2*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-8*I*e^(6*I*f*x + 6*I*e) + I*e^(4*I*f*x + 4*I*e) + 11*I*e^(2*I*f*x + 2*I*e) + 2*I))*e^(-4*I*f*x - 4*I*e)/(a^2*c*f)","B",0
979,1,306,0,0.482540," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(105 i \, \sqrt{\frac{1}{2}} a^{3} c f \sqrt{\frac{1}{a^{6} c f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(2240 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2240 i \, a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{6} c f^{2}}} + 2240 i\right)} e^{\left(-i \, f x - i \, e\right)}}{4096 \, a^{3} f}\right) - 105 i \, \sqrt{\frac{1}{2}} a^{3} c f \sqrt{\frac{1}{a^{6} c f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-2240 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 2240 i \, a^{3} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{6} c f^{2}}} + 2240 i\right)} e^{\left(-i \, f x - i \, e\right)}}{4096 \, a^{3} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-48 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 39 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 125 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 46 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{768 \, a^{3} c f}"," ",0,"1/768*(105*I*sqrt(1/2)*a^3*c*f*sqrt(1/(a^6*c*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4096*(sqrt(2)*sqrt(1/2)*(2240*I*a^3*f*e^(2*I*f*x + 2*I*e) + 2240*I*a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^6*c*f^2)) + 2240*I)*e^(-I*f*x - I*e)/(a^3*f)) - 105*I*sqrt(1/2)*a^3*c*f*sqrt(1/(a^6*c*f^2))*e^(6*I*f*x + 6*I*e)*log(1/4096*(sqrt(2)*sqrt(1/2)*(-2240*I*a^3*f*e^(2*I*f*x + 2*I*e) - 2240*I*a^3*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^6*c*f^2)) + 2240*I)*e^(-I*f*x - I*e)/(a^3*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-48*I*e^(8*I*f*x + 8*I*e) + 39*I*e^(6*I*f*x + 6*I*e) + 125*I*e^(4*I*f*x + 4*I*e) + 46*I*e^(2*I*f*x + 2*I*e) + 8*I))*e^(-6*I*f*x - 6*I*e)/(a^3*c*f)","A",0
980,1,62,0,0.475271," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-2 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 8 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, c^{2} f}"," ",0,"1/3*sqrt(2)*(-2*I*a^3*e^(4*I*f*x + 4*I*e) + 8*I*a^3*e^(2*I*f*x + 2*I*e) + 16*I*a^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","A",0
981,1,62,0,0.469771," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, c^{2} f}"," ",0,"1/3*sqrt(2)*(-I*a^2*e^(4*I*f*x + 4*I*e) + I*a^2*e^(2*I*f*x + 2*I*e) + 2*I*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","A",0
982,1,56,0,0.456494," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 2 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - i \, a\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{6 \, c^{2} f}"," ",0,"1/6*sqrt(2)*(-I*a*e^(4*I*f*x + 4*I*e) - 2*I*a*e^(2*I*f*x + 2*I*e) - I*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","B",0
983,1,297,0,0.449426," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(15 i \, \sqrt{\frac{1}{2}} a c^{2} f \sqrt{\frac{1}{a^{2} c^{3} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(20 i \, a c f e^{\left(2 i \, f x + 2 i \, e\right)} + 20 i \, a c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{2} c^{3} f^{2}}} + 20 i\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a c f}\right) - 15 i \, \sqrt{\frac{1}{2}} a c^{2} f \sqrt{\frac{1}{a^{2} c^{3} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-20 i \, a c f e^{\left(2 i \, f x + 2 i \, e\right)} - 20 i \, a c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{2} c^{3} f^{2}}} + 20 i\right)} e^{\left(-i \, f x - i \, e\right)}}{16 \, a c f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-2 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 16 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 11 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{48 \, a c^{2} f}"," ",0,"1/48*(15*I*sqrt(1/2)*a*c^2*f*sqrt(1/(a^2*c^3*f^2))*e^(2*I*f*x + 2*I*e)*log(1/16*(sqrt(2)*sqrt(1/2)*(20*I*a*c*f*e^(2*I*f*x + 2*I*e) + 20*I*a*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^2*c^3*f^2)) + 20*I)*e^(-I*f*x - I*e)/(a*c*f)) - 15*I*sqrt(1/2)*a*c^2*f*sqrt(1/(a^2*c^3*f^2))*e^(2*I*f*x + 2*I*e)*log(1/16*(sqrt(2)*sqrt(1/2)*(-20*I*a*c*f*e^(2*I*f*x + 2*I*e) - 20*I*a*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^2*c^3*f^2)) + 20*I)*e^(-I*f*x - I*e)/(a*c*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-2*I*e^(6*I*f*x + 6*I*e) - 16*I*e^(4*I*f*x + 4*I*e) - 11*I*e^(2*I*f*x + 2*I*e) + 3*I))*e^(-2*I*f*x - 2*I*e)/(a*c^2*f)","B",0
984,1,320,0,0.494287," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(105 i \, \sqrt{\frac{1}{2}} a^{2} c^{2} f \sqrt{\frac{1}{a^{4} c^{3} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(1120 i \, a^{2} c f e^{\left(2 i \, f x + 2 i \, e\right)} + 1120 i \, a^{2} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{4} c^{3} f^{2}}} + 1120 i\right)} e^{\left(-i \, f x - i \, e\right)}}{1024 \, a^{2} c f}\right) - 105 i \, \sqrt{\frac{1}{2}} a^{2} c^{2} f \sqrt{\frac{1}{a^{4} c^{3} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-1120 i \, a^{2} c f e^{\left(2 i \, f x + 2 i \, e\right)} - 1120 i \, a^{2} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{4} c^{3} f^{2}}} + 1120 i\right)} e^{\left(-i \, f x - i \, e\right)}}{1024 \, a^{2} c f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-8 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 88 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 41 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 45 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 6 i\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{384 \, a^{2} c^{2} f}"," ",0,"1/384*(105*I*sqrt(1/2)*a^2*c^2*f*sqrt(1/(a^4*c^3*f^2))*e^(4*I*f*x + 4*I*e)*log(1/1024*(sqrt(2)*sqrt(1/2)*(1120*I*a^2*c*f*e^(2*I*f*x + 2*I*e) + 1120*I*a^2*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^4*c^3*f^2)) + 1120*I)*e^(-I*f*x - I*e)/(a^2*c*f)) - 105*I*sqrt(1/2)*a^2*c^2*f*sqrt(1/(a^4*c^3*f^2))*e^(4*I*f*x + 4*I*e)*log(1/1024*(sqrt(2)*sqrt(1/2)*(-1120*I*a^2*c*f*e^(2*I*f*x + 2*I*e) - 1120*I*a^2*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^4*c^3*f^2)) + 1120*I)*e^(-I*f*x - I*e)/(a^2*c*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-8*I*e^(8*I*f*x + 8*I*e) - 88*I*e^(6*I*f*x + 6*I*e) - 41*I*e^(4*I*f*x + 4*I*e) + 45*I*e^(2*I*f*x + 2*I*e) + 6*I))*e^(-4*I*f*x - 4*I*e)/(a^2*c^2*f)","B",0
985,1,331,0,0.479116," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(315 i \, \sqrt{\frac{1}{2}} a^{3} c^{2} f \sqrt{\frac{1}{a^{6} c^{3} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(13440 i \, a^{3} c f e^{\left(2 i \, f x + 2 i \, e\right)} + 13440 i \, a^{3} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{6} c^{3} f^{2}}} + 13440 i\right)} e^{\left(-i \, f x - i \, e\right)}}{16384 \, a^{3} c f}\right) - 315 i \, \sqrt{\frac{1}{2}} a^{3} c^{2} f \sqrt{\frac{1}{a^{6} c^{3} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-13440 i \, a^{3} c f e^{\left(2 i \, f x + 2 i \, e\right)} - 13440 i \, a^{3} c f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{6} c^{3} f^{2}}} + 13440 i\right)} e^{\left(-i \, f x - i \, e\right)}}{16384 \, a^{3} c f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-16 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 224 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 43 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 215 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 58 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{1536 \, a^{3} c^{2} f}"," ",0,"1/1536*(315*I*sqrt(1/2)*a^3*c^2*f*sqrt(1/(a^6*c^3*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16384*(sqrt(2)*sqrt(1/2)*(13440*I*a^3*c*f*e^(2*I*f*x + 2*I*e) + 13440*I*a^3*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^6*c^3*f^2)) + 13440*I)*e^(-I*f*x - I*e)/(a^3*c*f)) - 315*I*sqrt(1/2)*a^3*c^2*f*sqrt(1/(a^6*c^3*f^2))*e^(6*I*f*x + 6*I*e)*log(1/16384*(sqrt(2)*sqrt(1/2)*(-13440*I*a^3*c*f*e^(2*I*f*x + 2*I*e) - 13440*I*a^3*c*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^6*c^3*f^2)) + 13440*I)*e^(-I*f*x - I*e)/(a^3*c*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-16*I*e^(10*I*f*x + 10*I*e) - 224*I*e^(8*I*f*x + 8*I*e) - 43*I*e^(6*I*f*x + 6*I*e) + 215*I*e^(4*I*f*x + 4*I*e) + 58*I*e^(2*I*f*x + 2*I*e) + 8*I))*e^(-6*I*f*x - 6*I*e)/(a^3*c^2*f)","A",0
986,1,76,0,0.440506," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-3 i \, a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 4 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{3}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{15 \, c^{3} f}"," ",0,"1/15*sqrt(2)*(-3*I*a^3*e^(6*I*f*x + 6*I*e) + I*a^3*e^(4*I*f*x + 4*I*e) - 4*I*a^3*e^(2*I*f*x + 2*I*e) - 8*I*a^3)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
987,1,76,0,0.463119," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-3 i \, a^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 4 i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a^{2}\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{30 \, c^{3} f}"," ",0,"1/30*sqrt(2)*(-3*I*a^2*e^(6*I*f*x + 6*I*e) - 4*I*a^2*e^(4*I*f*x + 4*I*e) + I*a^2*e^(2*I*f*x + 2*I*e) + 2*I*a^2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
988,1,68,0,0.465189," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, a e^{\left(4 i \, f x + 4 i \, e\right)} - 3 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - i \, a\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{20 \, c^{3} f}"," ",0,"1/20*sqrt(2)*(-I*a*e^(6*I*f*x + 6*I*e) - 3*I*a*e^(4*I*f*x + 4*I*e) - 3*I*a*e^(2*I*f*x + 2*I*e) - I*a)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","B",0
989,1,316,0,0.482620," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(105 i \, \sqrt{\frac{1}{2}} a c^{3} f \sqrt{\frac{1}{a^{2} c^{5} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(56 i \, a c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 56 i \, a c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{2} c^{5} f^{2}}} + 56 i\right)} e^{\left(-i \, f x - i \, e\right)}}{64 \, a c^{2} f}\right) - 105 i \, \sqrt{\frac{1}{2}} a c^{3} f \sqrt{\frac{1}{a^{2} c^{5} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-56 i \, a c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 56 i \, a c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{2} c^{5} f^{2}}} + 56 i\right)} e^{\left(-i \, f x - i \, e\right)}}{64 \, a c^{2} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-6 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 38 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 148 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 101 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 15 i\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{480 \, a c^{3} f}"," ",0,"1/480*(105*I*sqrt(1/2)*a*c^3*f*sqrt(1/(a^2*c^5*f^2))*e^(2*I*f*x + 2*I*e)*log(1/64*(sqrt(2)*sqrt(1/2)*(56*I*a*c^2*f*e^(2*I*f*x + 2*I*e) + 56*I*a*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^2*c^5*f^2)) + 56*I)*e^(-I*f*x - I*e)/(a*c^2*f)) - 105*I*sqrt(1/2)*a*c^3*f*sqrt(1/(a^2*c^5*f^2))*e^(2*I*f*x + 2*I*e)*log(1/64*(sqrt(2)*sqrt(1/2)*(-56*I*a*c^2*f*e^(2*I*f*x + 2*I*e) - 56*I*a*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^2*c^5*f^2)) + 56*I)*e^(-I*f*x - I*e)/(a*c^2*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-6*I*e^(8*I*f*x + 8*I*e) - 38*I*e^(6*I*f*x + 6*I*e) - 148*I*e^(4*I*f*x + 4*I*e) - 101*I*e^(2*I*f*x + 2*I*e) + 15*I))*e^(-2*I*f*x - 2*I*e)/(a*c^3*f)","B",0
990,1,339,0,0.543204," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(315 i \, \sqrt{\frac{1}{2}} a^{2} c^{3} f \sqrt{\frac{1}{a^{4} c^{5} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(4032 i \, a^{2} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4032 i \, a^{2} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{4} c^{5} f^{2}}} + 4032 i\right)} e^{\left(-i \, f x - i \, e\right)}}{4096 \, a^{2} c^{2} f}\right) - 315 i \, \sqrt{\frac{1}{2}} a^{2} c^{3} f \sqrt{\frac{1}{a^{4} c^{5} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-4032 i \, a^{2} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 4032 i \, a^{2} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{4} c^{5} f^{2}}} + 4032 i\right)} e^{\left(-i \, f x - i \, e\right)}}{4096 \, a^{2} c^{2} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-8 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 64 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 344 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 203 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 95 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 10 i\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{1280 \, a^{2} c^{3} f}"," ",0,"1/1280*(315*I*sqrt(1/2)*a^2*c^3*f*sqrt(1/(a^4*c^5*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4096*(sqrt(2)*sqrt(1/2)*(4032*I*a^2*c^2*f*e^(2*I*f*x + 2*I*e) + 4032*I*a^2*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^4*c^5*f^2)) + 4032*I)*e^(-I*f*x - I*e)/(a^2*c^2*f)) - 315*I*sqrt(1/2)*a^2*c^3*f*sqrt(1/(a^4*c^5*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4096*(sqrt(2)*sqrt(1/2)*(-4032*I*a^2*c^2*f*e^(2*I*f*x + 2*I*e) - 4032*I*a^2*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^4*c^5*f^2)) + 4032*I)*e^(-I*f*x - I*e)/(a^2*c^2*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-8*I*e^(10*I*f*x + 10*I*e) - 64*I*e^(8*I*f*x + 8*I*e) - 344*I*e^(6*I*f*x + 6*I*e) - 203*I*e^(4*I*f*x + 4*I*e) + 95*I*e^(2*I*f*x + 2*I*e) + 10*I))*e^(-4*I*f*x - 4*I*e)/(a^2*c^3*f)","A",0
991,1,350,0,0.514499," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(3465 i \, \sqrt{\frac{1}{2}} a^{3} c^{3} f \sqrt{\frac{1}{a^{6} c^{5} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(59136 i \, a^{3} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 59136 i \, a^{3} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{6} c^{5} f^{2}}} + 59136 i\right)} e^{\left(-i \, f x - i \, e\right)}}{65536 \, a^{3} c^{2} f}\right) - 3465 i \, \sqrt{\frac{1}{2}} a^{3} c^{3} f \sqrt{\frac{1}{a^{6} c^{5} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-59136 i \, a^{3} c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 59136 i \, a^{3} c^{2} f\right)} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{1}{a^{6} c^{5} f^{2}}} + 59136 i\right)} e^{\left(-i \, f x - i \, e\right)}}{65536 \, a^{3} c^{2} f}\right) + \sqrt{2} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-48 i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 464 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 3184 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 1433 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 1645 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 350 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 40 i\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{15360 \, a^{3} c^{3} f}"," ",0,"1/15360*(3465*I*sqrt(1/2)*a^3*c^3*f*sqrt(1/(a^6*c^5*f^2))*e^(6*I*f*x + 6*I*e)*log(1/65536*(sqrt(2)*sqrt(1/2)*(59136*I*a^3*c^2*f*e^(2*I*f*x + 2*I*e) + 59136*I*a^3*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^6*c^5*f^2)) + 59136*I)*e^(-I*f*x - I*e)/(a^3*c^2*f)) - 3465*I*sqrt(1/2)*a^3*c^3*f*sqrt(1/(a^6*c^5*f^2))*e^(6*I*f*x + 6*I*e)*log(1/65536*(sqrt(2)*sqrt(1/2)*(-59136*I*a^3*c^2*f*e^(2*I*f*x + 2*I*e) - 59136*I*a^3*c^2*f)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/(a^6*c^5*f^2)) + 59136*I)*e^(-I*f*x - I*e)/(a^3*c^2*f)) + sqrt(2)*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-48*I*e^(12*I*f*x + 12*I*e) - 464*I*e^(10*I*f*x + 10*I*e) - 3184*I*e^(8*I*f*x + 8*I*e) - 1433*I*e^(6*I*f*x + 6*I*e) + 1645*I*e^(4*I*f*x + 4*I*e) + 350*I*e^(2*I*f*x + 2*I*e) + 40*I))*e^(-6*I*f*x - 6*I*e)/(a^3*c^3*f)","A",0
992,1,357,0,0.458585," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{a^{5} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{5} c}{f^{2}}} {\left(4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, f\right)}}{a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}}\right) - 3 \, \sqrt{\frac{a^{5} c}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{5} c}{f^{2}}} {\left(-4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, f\right)}}{a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}}\right) - 2 \, {\left(10 i \, a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + 6 i \, a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/4*(3*sqrt(a^5*c/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a^2*e^(3*I*f*x + 3*I*e) + a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^5*c/f^2)*(4*I*f*e^(2*I*f*x + 2*I*e) - 4*I*f))/(a^2*e^(2*I*f*x + 2*I*e) + a^2)) - 3*sqrt(a^5*c/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a^2*e^(3*I*f*x + 3*I*e) + a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^5*c/f^2)*(-4*I*f*e^(2*I*f*x + 2*I*e) + 4*I*f))/(a^2*e^(2*I*f*x + 2*I*e) + a^2)) - 2*(10*I*a^2*e^(3*I*f*x + 3*I*e) + 6*I*a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
993,1,288,0,0.463386," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{8 i \, a \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(i \, f x + i \, e\right)} - 2 \, \sqrt{\frac{a^{3} c}{f^{2}}} f \log\left(\frac{2 \, {\left(4 \, {\left(a e^{\left(3 i \, f x + 3 i \, e\right)} + a e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{3} c}{f^{2}}} {\left(2 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, f\right)}\right)}}{a e^{\left(2 i \, f x + 2 i \, e\right)} + a}\right) + 2 \, \sqrt{\frac{a^{3} c}{f^{2}}} f \log\left(\frac{2 \, {\left(4 \, {\left(a e^{\left(3 i \, f x + 3 i \, e\right)} + a e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{3} c}{f^{2}}} {\left(-2 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, f\right)}\right)}}{a e^{\left(2 i \, f x + 2 i \, e\right)} + a}\right)}{4 \, f}"," ",0,"1/4*(8*I*a*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(I*f*x + I*e) - 2*sqrt(a^3*c/f^2)*f*log(2*(4*(a*e^(3*I*f*x + 3*I*e) + a*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^3*c/f^2)*(2*I*f*e^(2*I*f*x + 2*I*e) - 2*I*f))/(a*e^(2*I*f*x + 2*I*e) + a)) + 2*sqrt(a^3*c/f^2)*f*log(2*(4*(a*e^(3*I*f*x + 3*I*e) + a*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^3*c/f^2)*(-2*I*f*e^(2*I*f*x + 2*I*e) + 2*I*f))/(a*e^(2*I*f*x + 2*I*e) + a)))/f","B",0
994,1,215,0,0.589025," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{a c}{f^{2}}} \log\left(\frac{2 \, {\left(4 \, \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(3 i \, f x + 3 i \, e\right)} + e^{\left(i \, f x + i \, e\right)}\right)} + {\left(2 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, f\right)} \sqrt{\frac{a c}{f^{2}}}\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) + \frac{1}{2} \, \sqrt{\frac{a c}{f^{2}}} \log\left(\frac{2 \, {\left(4 \, \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(3 i \, f x + 3 i \, e\right)} + e^{\left(i \, f x + i \, e\right)}\right)} + {\left(-2 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, f\right)} \sqrt{\frac{a c}{f^{2}}}\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)"," ",0,"-1/2*sqrt(a*c/f^2)*log(2*(4*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(e^(3*I*f*x + 3*I*e) + e^(I*f*x + I*e)) + (2*I*f*e^(2*I*f*x + 2*I*e) - 2*I*f)*sqrt(a*c/f^2))/(e^(2*I*f*x + 2*I*e) + 1)) + 1/2*sqrt(a*c/f^2)*log(2*(4*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(e^(3*I*f*x + 3*I*e) + e^(I*f*x + I*e)) + (-2*I*f*e^(2*I*f*x + 2*I*e) + 2*I*f)*sqrt(a*c/f^2))/(e^(2*I*f*x + 2*I*e) + 1))","B",0
995,1,63,0,0.408161," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}"," ",0,"sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(I*e^(2*I*f*x + 2*I*e) + I)*e^(-I*f*x - I*e)/(a*f)","B",0
996,1,75,0,0.425866," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(3 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 4 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{6 \, a^{2} f}"," ",0,"1/6*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(3*I*e^(4*I*f*x + 4*I*e) + 4*I*e^(2*I*f*x + 2*I*e) + I)*e^(-3*I*f*x - 3*I*e)/(a^2*f)","A",0
997,1,86,0,0.426362," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(15 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 25 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 13 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{60 \, a^{3} f}"," ",0,"1/60*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(15*I*e^(6*I*f*x + 6*I*e) + 25*I*e^(4*I*f*x + 4*I*e) + 13*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(-5*I*f*x - 5*I*e)/(a^3*f)","A",0
998,1,97,0,0.461263," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(35 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 70 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 56 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 26 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 5 i\right)} e^{\left(-7 i \, f x - 7 i \, e\right)}}{280 \, a^{4} f}"," ",0,"1/280*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(35*I*e^(8*I*f*x + 8*I*e) + 70*I*e^(6*I*f*x + 6*I*e) + 56*I*e^(4*I*f*x + 4*I*e) + 26*I*e^(2*I*f*x + 2*I*e) + 5*I)*e^(-7*I*f*x - 7*I*e)/(a^4*f)","A",0
999,1,428,0,0.499065," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{a^{5} c^{3}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a^{2} c e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{5} c^{3}}{f^{2}}} {\left(4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, f\right)}}{a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c}\right) - 3 \, \sqrt{\frac{a^{5} c^{3}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a^{2} c e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{5} c^{3}}{f^{2}}} {\left(-4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, f\right)}}{a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c}\right) - 2 \, {\left(-6 i \, a^{2} c e^{\left(5 i \, f x + 5 i \, e\right)} + 16 i \, a^{2} c e^{\left(3 i \, f x + 3 i \, e\right)} + 6 i \, a^{2} c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/12*(3*sqrt(a^5*c^3/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a^2*c*e^(3*I*f*x + 3*I*e) + a^2*c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^5*c^3/f^2)*(4*I*f*e^(2*I*f*x + 2*I*e) - 4*I*f))/(a^2*c*e^(2*I*f*x + 2*I*e) + a^2*c)) - 3*sqrt(a^5*c^3/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a^2*c*e^(3*I*f*x + 3*I*e) + a^2*c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^5*c^3/f^2)*(-4*I*f*e^(2*I*f*x + 2*I*e) + 4*I*f))/(a^2*c*e^(2*I*f*x + 2*I*e) + a^2*c)) - 2*(-6*I*a^2*c*e^(5*I*f*x + 5*I*e) + 16*I*a^2*c*e^(3*I*f*x + 3*I*e) + 6*I*a^2*c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1000,1,356,0,0.467286," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{a^{3} c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a c e^{\left(3 i \, f x + 3 i \, e\right)} + a c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{3} c^{3}}{f^{2}}} {\left(4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, f\right)}}{a c e^{\left(2 i \, f x + 2 i \, e\right)} + a c}\right) - \sqrt{\frac{a^{3} c^{3}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a c e^{\left(3 i \, f x + 3 i \, e\right)} + a c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{3} c^{3}}{f^{2}}} {\left(-4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, f\right)}}{a c e^{\left(2 i \, f x + 2 i \, e\right)} + a c}\right) - 2 \, {\left(-2 i \, a c e^{\left(3 i \, f x + 3 i \, e\right)} + 2 i \, a c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/4*(sqrt(a^3*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a*c*e^(3*I*f*x + 3*I*e) + a*c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^3*c^3/f^2)*(4*I*f*e^(2*I*f*x + 2*I*e) - 4*I*f))/(a*c*e^(2*I*f*x + 2*I*e) + a*c)) - sqrt(a^3*c^3/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a*c*e^(3*I*f*x + 3*I*e) + a*c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^3*c^3/f^2)*(-4*I*f*e^(2*I*f*x + 2*I*e) + 4*I*f))/(a*c*e^(2*I*f*x + 2*I*e) + a*c)) - 2*(-2*I*a*c*e^(3*I*f*x + 3*I*e) + 2*I*a*c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
1001,1,288,0,0.472633," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{-8 i \, c \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(i \, f x + i \, e\right)} - 2 \, \sqrt{\frac{a c^{3}}{f^{2}}} f \log\left(\frac{2 \, {\left(4 \, {\left(c e^{\left(3 i \, f x + 3 i \, e\right)} + c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a c^{3}}{f^{2}}} {\left(2 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, f\right)}\right)}}{c e^{\left(2 i \, f x + 2 i \, e\right)} + c}\right) + 2 \, \sqrt{\frac{a c^{3}}{f^{2}}} f \log\left(\frac{2 \, {\left(4 \, {\left(c e^{\left(3 i \, f x + 3 i \, e\right)} + c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a c^{3}}{f^{2}}} {\left(-2 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, f\right)}\right)}}{c e^{\left(2 i \, f x + 2 i \, e\right)} + c}\right)}{4 \, f}"," ",0,"1/4*(-8*I*c*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(I*f*x + I*e) - 2*sqrt(a*c^3/f^2)*f*log(2*(4*(c*e^(3*I*f*x + 3*I*e) + c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a*c^3/f^2)*(2*I*f*e^(2*I*f*x + 2*I*e) - 2*I*f))/(c*e^(2*I*f*x + 2*I*e) + c)) + 2*sqrt(a*c^3/f^2)*f*log(2*(4*(c*e^(3*I*f*x + 3*I*e) + c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a*c^3/f^2)*(-2*I*f*e^(2*I*f*x + 2*I*e) + 2*I*f))/(c*e^(2*I*f*x + 2*I*e) + c)))/f","B",0
1002,1,336,0,0.464814," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a f \sqrt{\frac{c^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left(4 \, {\left(c e^{\left(3 i \, f x + 3 i \, e\right)} + c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a f\right)} \sqrt{\frac{c^{3}}{a f^{2}}}\right)}}{c e^{\left(2 i \, f x + 2 i \, e\right)} + c}\right) - a f \sqrt{\frac{c^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left(4 \, {\left(c e^{\left(3 i \, f x + 3 i \, e\right)} + c e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a f\right)} \sqrt{\frac{c^{3}}{a f^{2}}}\right)}}{c e^{\left(2 i \, f x + 2 i \, e\right)} + c}\right) + {\left(4 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a f}"," ",0,"1/2*(a*f*sqrt(c^3/(a*f^2))*e^(I*f*x + I*e)*log(2*(4*(c*e^(3*I*f*x + 3*I*e) + c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*a*f*e^(2*I*f*x + 2*I*e) - 2*I*a*f)*sqrt(c^3/(a*f^2)))/(c*e^(2*I*f*x + 2*I*e) + c)) - a*f*sqrt(c^3/(a*f^2))*e^(I*f*x + I*e)*log(2*(4*(c*e^(3*I*f*x + 3*I*e) + c*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*a*f*e^(2*I*f*x + 2*I*e) + 2*I*a*f)*sqrt(c^3/(a*f^2)))/(c*e^(2*I*f*x + 2*I*e) + c)) + (4*I*c*e^(2*I*f*x + 2*I*e) + 4*I*c)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)","B",0
1003,1,67,0,0.410887," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-3 i \, f x - 3 i \, e\right)}}{3 \, a^{2} f}"," ",0,"1/3*(I*c*e^(2*I*f*x + 2*I*e) + I*c)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-3*I*f*x - 3*I*e)/(a^2*f)","B",0
1004,1,79,0,0.469840," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 i \, c e^{\left(4 i \, f x + 4 i \, e\right)} + 8 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, c\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-5 i \, f x - 5 i \, e\right)}}{30 \, a^{3} f}"," ",0,"1/30*(5*I*c*e^(4*I*f*x + 4*I*e) + 8*I*c*e^(2*I*f*x + 2*I*e) + 3*I*c)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-5*I*f*x - 5*I*e)/(a^3*f)","A",0
1005,1,91,0,0.440053," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(35 i \, c e^{\left(6 i \, f x + 6 i \, e\right)} + 77 i \, c e^{\left(4 i \, f x + 4 i \, e\right)} + 57 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 15 i \, c\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-7 i \, f x - 7 i \, e\right)}}{420 \, a^{4} f}"," ",0,"1/420*(35*I*c*e^(6*I*f*x + 6*I*e) + 77*I*c*e^(4*I*f*x + 4*I*e) + 57*I*c*e^(2*I*f*x + 2*I*e) + 15*I*c)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-7*I*f*x - 7*I*e)/(a^4*f)","A",0
1006,1,103,0,0.508584," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(105 i \, c e^{\left(8 i \, f x + 8 i \, e\right)} + 294 i \, c e^{\left(6 i \, f x + 6 i \, e\right)} + 324 i \, c e^{\left(4 i \, f x + 4 i \, e\right)} + 170 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + 35 i \, c\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-9 i \, f x - 9 i \, e\right)}}{2520 \, a^{5} f}"," ",0,"1/2520*(105*I*c*e^(8*I*f*x + 8*I*e) + 294*I*c*e^(6*I*f*x + 6*I*e) + 324*I*c*e^(4*I*f*x + 4*I*e) + 170*I*c*e^(2*I*f*x + 2*I*e) + 35*I*c)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-9*I*f*x - 9*I*e)/(a^5*f)","A",0
1007,1,505,0,0.494520," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{a^{5} c^{5}}{f^{2}}} {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{32 \, {\left(a^{2} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{5} c^{5}}{f^{2}}} {\left(16 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, f\right)}}{4 \, {\left(a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c^{2}\right)}}\right) - 3 \, \sqrt{\frac{a^{5} c^{5}}{f^{2}}} {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{32 \, {\left(a^{2} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{5} c^{5}}{f^{2}}} {\left(-16 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, f\right)}}{4 \, {\left(a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} c^{2}\right)}}\right) - 4 \, {\left(-3 i \, a^{2} c^{2} e^{\left(7 i \, f x + 7 i \, e\right)} - 11 i \, a^{2} c^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + 11 i \, a^{2} c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + 3 i \, a^{2} c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{16 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/16*(3*sqrt(a^5*c^5/f^2)*(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(32*(a^2*c^2*e^(3*I*f*x + 3*I*e) + a^2*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^5*c^5/f^2)*(16*I*f*e^(2*I*f*x + 2*I*e) - 16*I*f))/(a^2*c^2*e^(2*I*f*x + 2*I*e) + a^2*c^2)) - 3*sqrt(a^5*c^5/f^2)*(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)*log(1/4*(32*(a^2*c^2*e^(3*I*f*x + 3*I*e) + a^2*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^5*c^5/f^2)*(-16*I*f*e^(2*I*f*x + 2*I*e) + 16*I*f))/(a^2*c^2*e^(2*I*f*x + 2*I*e) + a^2*c^2)) - 4*(-3*I*a^2*c^2*e^(7*I*f*x + 7*I*e) - 11*I*a^2*c^2*e^(5*I*f*x + 5*I*e) + 11*I*a^2*c^2*e^(3*I*f*x + 3*I*e) + 3*I*a^2*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1008,1,428,0,0.952451," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{a^{3} c^{5}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{3} c^{5}}{f^{2}}} {\left(4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, f\right)}}{a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a c^{2}}\right) - 3 \, \sqrt{\frac{a^{3} c^{5}}{f^{2}}} {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(a c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{3} c^{5}}{f^{2}}} {\left(-4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, f\right)}}{a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a c^{2}}\right) - 2 \, {\left(-6 i \, a c^{2} e^{\left(5 i \, f x + 5 i \, e\right)} - 16 i \, a c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + 6 i \, a c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/12*(3*sqrt(a^3*c^5/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a*c^2*e^(3*I*f*x + 3*I*e) + a*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^3*c^5/f^2)*(4*I*f*e^(2*I*f*x + 2*I*e) - 4*I*f))/(a*c^2*e^(2*I*f*x + 2*I*e) + a*c^2)) - 3*sqrt(a^3*c^5/f^2)*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*log((8*(a*c^2*e^(3*I*f*x + 3*I*e) + a*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^3*c^5/f^2)*(-4*I*f*e^(2*I*f*x + 2*I*e) + 4*I*f))/(a*c^2*e^(2*I*f*x + 2*I*e) + a*c^2)) - 2*(-6*I*a*c^2*e^(5*I*f*x + 5*I*e) - 16*I*a*c^2*e^(3*I*f*x + 3*I*e) + 6*I*a*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1009,1,357,0,0.455512," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{a c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a c^{5}}{f^{2}}} {\left(4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, f\right)}}{c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2}}\right) - 3 \, \sqrt{\frac{a c^{5}}{f^{2}}} {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \log\left(\frac{8 \, {\left(c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a c^{5}}{f^{2}}} {\left(-4 i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, f\right)}}{c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2}}\right) - 2 \, {\left(-6 i \, c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} - 10 i \, c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/4*(3*sqrt(a*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((8*(c^2*e^(3*I*f*x + 3*I*e) + c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a*c^5/f^2)*(4*I*f*e^(2*I*f*x + 2*I*e) - 4*I*f))/(c^2*e^(2*I*f*x + 2*I*e) + c^2)) - 3*sqrt(a*c^5/f^2)*(f*e^(2*I*f*x + 2*I*e) + f)*log((8*(c^2*e^(3*I*f*x + 3*I*e) + c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a*c^5/f^2)*(-4*I*f*e^(2*I*f*x + 2*I*e) + 4*I*f))/(c^2*e^(2*I*f*x + 2*I*e) + c^2)) - 2*(-6*I*c^2*e^(3*I*f*x + 3*I*e) - 10*I*c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
1010,1,357,0,0.462593," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{c^{5}}{a f^{2}}} a f e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left(4 \, {\left(c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a f\right)} \sqrt{\frac{c^{5}}{a f^{2}}}\right)}}{c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2}}\right) - 3 \, \sqrt{\frac{c^{5}}{a f^{2}}} a f e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left(4 \, {\left(c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a f\right)} \sqrt{\frac{c^{5}}{a f^{2}}}\right)}}{c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2}}\right) + {\left(12 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, c^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a f}"," ",0,"1/2*(3*sqrt(c^5/(a*f^2))*a*f*e^(I*f*x + I*e)*log(2*(4*(c^2*e^(3*I*f*x + 3*I*e) + c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*a*f*e^(2*I*f*x + 2*I*e) - 2*I*a*f)*sqrt(c^5/(a*f^2)))/(c^2*e^(2*I*f*x + 2*I*e) + c^2)) - 3*sqrt(c^5/(a*f^2))*a*f*e^(I*f*x + I*e)*log(2*(4*(c^2*e^(3*I*f*x + 3*I*e) + c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*a*f*e^(2*I*f*x + 2*I*e) + 2*I*a*f)*sqrt(c^5/(a*f^2)))/(c^2*e^(2*I*f*x + 2*I*e) + c^2)) + (12*I*c^2*e^(2*I*f*x + 2*I*e) + 8*I*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)","B",0
1011,1,384,0,0.559619," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} f \sqrt{\frac{c^{5}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{2 \, {\left(4 \, {\left(c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a^{2} f\right)} \sqrt{\frac{c^{5}}{a^{3} f^{2}}}\right)}}{c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2}}\right) - 3 \, a^{2} f \sqrt{\frac{c^{5}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{2 \, {\left(4 \, {\left(c^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + c^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a^{2} f\right)} \sqrt{\frac{c^{5}}{a^{3} f^{2}}}\right)}}{c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2}}\right) - {\left(-12 i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 8 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{6 \, a^{2} f}"," ",0,"-1/6*(3*a^2*f*sqrt(c^5/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(2*(4*(c^2*e^(3*I*f*x + 3*I*e) + c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*a^2*f*e^(2*I*f*x + 2*I*e) - 2*I*a^2*f)*sqrt(c^5/(a^3*f^2)))/(c^2*e^(2*I*f*x + 2*I*e) + c^2)) - 3*a^2*f*sqrt(c^5/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(2*(4*(c^2*e^(3*I*f*x + 3*I*e) + c^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*a^2*f*e^(2*I*f*x + 2*I*e) + 2*I*a^2*f)*sqrt(c^5/(a^3*f^2)))/(c^2*e^(2*I*f*x + 2*I*e) + c^2)) - (-12*I*c^2*e^(4*I*f*x + 4*I*e) - 8*I*c^2*e^(2*I*f*x + 2*I*e) + 4*I*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-3*I*f*x - 3*I*e)/(a^2*f)","B",0
1012,1,71,0,0.432120," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-5 i \, f x - 5 i \, e\right)}}{5 \, a^{3} f}"," ",0,"1/5*(I*c^2*e^(2*I*f*x + 2*I*e) + I*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-5*I*f*x - 5*I*e)/(a^3*f)","B",0
1013,1,85,0,0.585325," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(7 i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 12 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 5 i \, c^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-7 i \, f x - 7 i \, e\right)}}{70 \, a^{4} f}"," ",0,"1/70*(7*I*c^2*e^(4*I*f*x + 4*I*e) + 12*I*c^2*e^(2*I*f*x + 2*I*e) + 5*I*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-7*I*f*x - 7*I*e)/(a^4*f)","A",0
1014,1,99,0,0.416293," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(63 i \, c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 153 i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 125 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 35 i \, c^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-9 i \, f x - 9 i \, e\right)}}{1260 \, a^{5} f}"," ",0,"1/1260*(63*I*c^2*e^(6*I*f*x + 6*I*e) + 153*I*c^2*e^(4*I*f*x + 4*I*e) + 125*I*c^2*e^(2*I*f*x + 2*I*e) + 35*I*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-9*I*f*x - 9*I*e)/(a^5*f)","A",0
1015,1,113,0,0.448173," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left(231 i \, c^{2} e^{\left(8 i \, f x + 8 i \, e\right)} + 726 i \, c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 880 i \, c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 490 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 105 i \, c^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(-11 i \, f x - 11 i \, e\right)}}{9240 \, a^{6} f}"," ",0,"1/9240*(231*I*c^2*e^(8*I*f*x + 8*I*e) + 726*I*c^2*e^(6*I*f*x + 6*I*e) + 880*I*c^2*e^(4*I*f*x + 4*I*e) + 490*I*c^2*e^(2*I*f*x + 2*I*e) + 105*I*c^2)*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*e^(-11*I*f*x - 11*I*e)/(a^6*f)","A",0
1016,1,392,0,0.478100," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{a^{7}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)} \log\left(\frac{8 \, {\left(a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{7}}{c f^{2}}} {\left(4 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, c f\right)}}{a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3}}\right) - 15 \, \sqrt{\frac{a^{7}}{c f^{2}}} {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)} \log\left(\frac{8 \, {\left(a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{7}}{c f^{2}}} {\left(-4 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c f\right)}}{a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3}}\right) + 2 \, {\left(-16 i \, a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} - 50 i \, a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} - 30 i \, a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(c f e^{\left(2 i \, f x + 2 i \, e\right)} + c f\right)}}"," ",0,"1/4*(15*sqrt(a^7/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) + c*f)*log((8*(a^3*e^(3*I*f*x + 3*I*e) + a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^7/(c*f^2))*(4*I*c*f*e^(2*I*f*x + 2*I*e) - 4*I*c*f))/(a^3*e^(2*I*f*x + 2*I*e) + a^3)) - 15*sqrt(a^7/(c*f^2))*(c*f*e^(2*I*f*x + 2*I*e) + c*f)*log((8*(a^3*e^(3*I*f*x + 3*I*e) + a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^7/(c*f^2))*(-4*I*c*f*e^(2*I*f*x + 2*I*e) + 4*I*c*f))/(a^3*e^(2*I*f*x + 2*I*e) + a^3)) + 2*(-16*I*a^3*e^(5*I*f*x + 5*I*e) - 50*I*a^3*e^(3*I*f*x + 3*I*e) - 30*I*a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c*f*e^(2*I*f*x + 2*I*e) + c*f)","B",0
1017,1,339,0,0.627668," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{a^{5}}{c f^{2}}} c f \log\left(\frac{2 \, {\left(4 \, {\left(a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c f\right)} \sqrt{\frac{a^{5}}{c f^{2}}}\right)}}{a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}}\right) - 3 \, \sqrt{\frac{a^{5}}{c f^{2}}} c f \log\left(\frac{2 \, {\left(4 \, {\left(a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c f\right)} \sqrt{\frac{a^{5}}{c f^{2}}}\right)}}{a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}}\right) + {\left(-8 i \, a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} - 12 i \, a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{2 \, c f}"," ",0,"1/2*(3*sqrt(a^5/(c*f^2))*c*f*log(2*(4*(a^2*e^(3*I*f*x + 3*I*e) + a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*c*f*e^(2*I*f*x + 2*I*e) - 2*I*c*f)*sqrt(a^5/(c*f^2)))/(a^2*e^(2*I*f*x + 2*I*e) + a^2)) - 3*sqrt(a^5/(c*f^2))*c*f*log(2*(4*(a^2*e^(3*I*f*x + 3*I*e) + a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*c*f*e^(2*I*f*x + 2*I*e) + 2*I*c*f)*sqrt(a^5/(c*f^2)))/(a^2*e^(2*I*f*x + 2*I*e) + a^2)) + (-8*I*a^2*e^(3*I*f*x + 3*I*e) - 12*I*a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c*f)","B",0
1018,1,318,0,0.456510," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{c f \sqrt{\frac{a^{3}}{c f^{2}}} \log\left(\frac{2 \, {\left(4 \, {\left(a e^{\left(3 i \, f x + 3 i \, e\right)} + a e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c f\right)} \sqrt{\frac{a^{3}}{c f^{2}}}\right)}}{a e^{\left(2 i \, f x + 2 i \, e\right)} + a}\right) - c f \sqrt{\frac{a^{3}}{c f^{2}}} \log\left(\frac{2 \, {\left(4 \, {\left(a e^{\left(3 i \, f x + 3 i \, e\right)} + a e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, c f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c f\right)} \sqrt{\frac{a^{3}}{c f^{2}}}\right)}}{a e^{\left(2 i \, f x + 2 i \, e\right)} + a}\right) + {\left(-4 i \, a e^{\left(3 i \, f x + 3 i \, e\right)} - 4 i \, a e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{2 \, c f}"," ",0,"1/2*(c*f*sqrt(a^3/(c*f^2))*log(2*(4*(a*e^(3*I*f*x + 3*I*e) + a*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*c*f*e^(2*I*f*x + 2*I*e) - 2*I*c*f)*sqrt(a^3/(c*f^2)))/(a*e^(2*I*f*x + 2*I*e) + a)) - c*f*sqrt(a^3/(c*f^2))*log(2*(4*(a*e^(3*I*f*x + 3*I*e) + a*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*c*f*e^(2*I*f*x + 2*I*e) + 2*I*c*f)*sqrt(a^3/(c*f^2)))/(a*e^(2*I*f*x + 2*I*e) + a)) + (-4*I*a*e^(3*I*f*x + 3*I*e) - 4*I*a*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c*f)","B",0
1019,1,64,0,0.419304," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(3 i \, f x + 3 i \, e\right)} - i \, e^{\left(i \, f x + i \, e\right)}\right)}}{c f}"," ",0,"sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(3*I*f*x + 3*I*e) - I*e^(I*f*x + I*e))/(c*f)","B",0
1020,1,67,0,0.442684," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(4 i \, f x + 4 i \, e\right)} + i\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a c f}"," ",0,"1/2*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(4*I*f*x + 4*I*e) + I)*e^(-I*f*x - I*e)/(a*c*f)","A",0
1021,1,111,0,0.423252," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-3 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 4 i \, e^{\left(5 i \, f x + 5 i \, e\right)} + 3 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 4 i \, e^{\left(3 i \, f x + 3 i \, e\right)} + 7 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{12 \, a^{2} c f}"," ",0,"1/12*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-3*I*e^(6*I*f*x + 6*I*e) - 4*I*e^(5*I*f*x + 5*I*e) + 3*I*e^(4*I*f*x + 4*I*e) - 4*I*e^(3*I*f*x + 3*I*e) + 7*I*e^(2*I*f*x + 2*I*e) + I)*e^(-3*I*f*x - 3*I*e)/(a^2*c*f)","A",0
1022,1,122,0,0.494009," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-5 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 16 i \, e^{\left(7 i \, f x + 7 i \, e\right)} + 10 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 16 i \, e^{\left(5 i \, f x + 5 i \, e\right)} + 20 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 6 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{40 \, a^{3} c f}"," ",0,"1/40*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-5*I*e^(8*I*f*x + 8*I*e) - 16*I*e^(7*I*f*x + 7*I*e) + 10*I*e^(6*I*f*x + 6*I*e) - 16*I*e^(5*I*f*x + 5*I*e) + 20*I*e^(4*I*f*x + 4*I*e) + 6*I*e^(2*I*f*x + 2*I*e) + I)*e^(-5*I*f*x - 5*I*e)/(a^3*c*f)","A",0
1023,1,133,0,0.427806," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-35 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 208 i \, e^{\left(9 i \, f x + 9 i \, e\right)} + 105 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 208 i \, e^{\left(7 i \, f x + 7 i \, e\right)} + 210 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 98 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 33 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 5 i\right)} e^{\left(-7 i \, f x - 7 i \, e\right)}}{560 \, a^{4} c f}"," ",0,"1/560*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-35*I*e^(10*I*f*x + 10*I*e) - 208*I*e^(9*I*f*x + 9*I*e) + 105*I*e^(8*I*f*x + 8*I*e) - 208*I*e^(7*I*f*x + 7*I*e) + 210*I*e^(6*I*f*x + 6*I*e) + 98*I*e^(4*I*f*x + 4*I*e) + 33*I*e^(2*I*f*x + 2*I*e) + 5*I)*e^(-7*I*f*x - 7*I*e)/(a^4*c*f)","A",0
1024,1,426,0,0.504327," ","integrate((a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{\frac{a^{9}}{c^{3} f^{2}}} {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)} \log\left(\frac{8 \, {\left(a^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{4} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{9}}{c^{3} f^{2}}} {\left(4 i \, c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, c^{2} f\right)}}{a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{4}}\right) - 105 \, \sqrt{\frac{a^{9}}{c^{3} f^{2}}} {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)} \log\left(\frac{8 \, {\left(a^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{4} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + \sqrt{\frac{a^{9}}{c^{3} f^{2}}} {\left(-4 i \, c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c^{2} f\right)}}{a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{4}}\right) - 2 \, {\left(-16 i \, a^{4} e^{\left(7 i \, f x + 7 i \, e\right)} + 112 i \, a^{4} e^{\left(5 i \, f x + 5 i \, e\right)} + 350 i \, a^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + 210 i \, a^{4} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} f\right)}}"," ",0,"-1/12*(105*sqrt(a^9/(c^3*f^2))*(c^2*f*e^(2*I*f*x + 2*I*e) + c^2*f)*log((8*(a^4*e^(3*I*f*x + 3*I*e) + a^4*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^9/(c^3*f^2))*(4*I*c^2*f*e^(2*I*f*x + 2*I*e) - 4*I*c^2*f))/(a^4*e^(2*I*f*x + 2*I*e) + a^4)) - 105*sqrt(a^9/(c^3*f^2))*(c^2*f*e^(2*I*f*x + 2*I*e) + c^2*f)*log((8*(a^4*e^(3*I*f*x + 3*I*e) + a^4*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(a^9/(c^3*f^2))*(-4*I*c^2*f*e^(2*I*f*x + 2*I*e) + 4*I*c^2*f))/(a^4*e^(2*I*f*x + 2*I*e) + a^4)) - 2*(-16*I*a^4*e^(7*I*f*x + 7*I*e) + 112*I*a^4*e^(5*I*f*x + 5*I*e) + 350*I*a^4*e^(3*I*f*x + 3*I*e) + 210*I*a^4*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2*f*e^(2*I*f*x + 2*I*e) + c^2*f)","B",0
1025,1,366,0,0.663536," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{a^{7}}{c^{3} f^{2}}} c^{2} f \log\left(\frac{2 \, {\left(4 \, {\left(a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c^{2} f\right)} \sqrt{\frac{a^{7}}{c^{3} f^{2}}}\right)}}{a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3}}\right) - 15 \, \sqrt{\frac{a^{7}}{c^{3} f^{2}}} c^{2} f \log\left(\frac{2 \, {\left(4 \, {\left(a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c^{2} f\right)} \sqrt{\frac{a^{7}}{c^{3} f^{2}}}\right)}}{a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3}}\right) - {\left(-8 i \, a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} + 40 i \, a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + 60 i \, a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{6 \, c^{2} f}"," ",0,"-1/6*(15*sqrt(a^7/(c^3*f^2))*c^2*f*log(2*(4*(a^3*e^(3*I*f*x + 3*I*e) + a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*c^2*f*e^(2*I*f*x + 2*I*e) - 2*I*c^2*f)*sqrt(a^7/(c^3*f^2)))/(a^3*e^(2*I*f*x + 2*I*e) + a^3)) - 15*sqrt(a^7/(c^3*f^2))*c^2*f*log(2*(4*(a^3*e^(3*I*f*x + 3*I*e) + a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*c^2*f*e^(2*I*f*x + 2*I*e) + 2*I*c^2*f)*sqrt(a^7/(c^3*f^2)))/(a^3*e^(2*I*f*x + 2*I*e) + a^3)) - (-8*I*a^3*e^(5*I*f*x + 5*I*e) + 40*I*a^3*e^(3*I*f*x + 3*I*e) + 60*I*a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2*f)","B",0
1026,1,366,0,0.518085," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, c^{2} f \sqrt{\frac{a^{5}}{c^{3} f^{2}}} \log\left(\frac{2 \, {\left(4 \, {\left(a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c^{2} f\right)} \sqrt{\frac{a^{5}}{c^{3} f^{2}}}\right)}}{a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}}\right) - 3 \, c^{2} f \sqrt{\frac{a^{5}}{c^{3} f^{2}}} \log\left(\frac{2 \, {\left(4 \, {\left(a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, c^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c^{2} f\right)} \sqrt{\frac{a^{5}}{c^{3} f^{2}}}\right)}}{a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}}\right) - {\left(-4 i \, a^{2} e^{\left(5 i \, f x + 5 i \, e\right)} + 8 i \, a^{2} e^{\left(3 i \, f x + 3 i \, e\right)} + 12 i \, a^{2} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{6 \, c^{2} f}"," ",0,"-1/6*(3*c^2*f*sqrt(a^5/(c^3*f^2))*log(2*(4*(a^2*e^(3*I*f*x + 3*I*e) + a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*c^2*f*e^(2*I*f*x + 2*I*e) - 2*I*c^2*f)*sqrt(a^5/(c^3*f^2)))/(a^2*e^(2*I*f*x + 2*I*e) + a^2)) - 3*c^2*f*sqrt(a^5/(c^3*f^2))*log(2*(4*(a^2*e^(3*I*f*x + 3*I*e) + a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*c^2*f*e^(2*I*f*x + 2*I*e) + 2*I*c^2*f)*sqrt(a^5/(c^3*f^2)))/(a^2*e^(2*I*f*x + 2*I*e) + a^2)) - (-4*I*a^2*e^(5*I*f*x + 5*I*e) + 8*I*a^2*e^(3*I*f*x + 3*I*e) + 12*I*a^2*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2*f)","B",0
1027,1,67,0,0.430387," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a e^{\left(5 i \, f x + 5 i \, e\right)} - i \, a e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{3 \, c^{2} f}"," ",0,"1/3*(-I*a*e^(5*I*f*x + 5*I*e) - I*a*e^(3*I*f*x + 3*I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^2*f)","B",0
1028,1,76,0,0.521721," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(5 i \, f x + 5 i \, e\right)} - 4 i \, e^{\left(3 i \, f x + 3 i \, e\right)} - 3 i \, e^{\left(i \, f x + i \, e\right)}\right)}}{6 \, c^{2} f}"," ",0,"1/6*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(5*I*f*x + 5*I*e) - 4*I*e^(3*I*f*x + 3*I*e) - 3*I*e^(I*f*x + I*e))/(c^2*f)","A",0
1029,1,111,0,0.474874," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 7 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 4 i \, e^{\left(3 i \, f x + 3 i \, e\right)} - 3 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, e^{\left(i \, f x + i \, e\right)} + 3 i\right)} e^{\left(-i \, f x - i \, e\right)}}{12 \, a c^{2} f}"," ",0,"1/12*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(6*I*f*x + 6*I*e) - 7*I*e^(4*I*f*x + 4*I*e) + 4*I*e^(3*I*f*x + 3*I*e) - 3*I*e^(2*I*f*x + 2*I*e) + 4*I*e^(I*f*x + I*e) + 3*I)*e^(-I*f*x - I*e)/(a*c^2*f)","A",0
1030,1,89,0,0.475380," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 10 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 10 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{24 \, a^{2} c^{2} f}"," ",0,"1/24*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(8*I*f*x + 8*I*e) - 10*I*e^(6*I*f*x + 6*I*e) + 10*I*e^(2*I*f*x + 2*I*e) + I)*e^(-3*I*f*x - 3*I*e)/(a^2*c^2*f)","A",0
1031,1,133,0,0.429993," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-5 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 65 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 48 i \, e^{\left(7 i \, f x + 7 i \, e\right)} + 30 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 48 i \, e^{\left(5 i \, f x + 5 i \, e\right)} + 110 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 23 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{240 \, a^{3} c^{2} f}"," ",0,"1/240*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-5*I*e^(10*I*f*x + 10*I*e) - 65*I*e^(8*I*f*x + 8*I*e) - 48*I*e^(7*I*f*x + 7*I*e) + 30*I*e^(6*I*f*x + 6*I*e) - 48*I*e^(5*I*f*x + 5*I*e) + 110*I*e^(4*I*f*x + 4*I*e) + 23*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(-5*I*f*x - 5*I*e)/(a^3*c^2*f)","A",0
1032,1,144,0,0.470280," ","integrate(1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-7 i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 112 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 192 i \, e^{\left(9 i \, f x + 9 i \, e\right)} + 105 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 192 i \, e^{\left(7 i \, f x + 7 i \, e\right)} + 280 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 91 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 24 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(-7 i \, f x - 7 i \, e\right)}}{672 \, a^{4} c^{2} f}"," ",0,"1/672*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-7*I*e^(12*I*f*x + 12*I*e) - 112*I*e^(10*I*f*x + 10*I*e) - 192*I*e^(9*I*f*x + 9*I*e) + 105*I*e^(8*I*f*x + 8*I*e) - 192*I*e^(7*I*f*x + 7*I*e) + 280*I*e^(6*I*f*x + 6*I*e) + 91*I*e^(4*I*f*x + 4*I*e) + 24*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(-7*I*f*x - 7*I*e)/(a^4*c^2*f)","A",0
1033,1,440,0,0.499299," ","integrate((a+I*a*tan(f*x+e))^(11/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{315 \, {\left(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{3} f\right)} \sqrt{\frac{a^{11}}{c^{5} f^{2}}} \log\left(\frac{8 \, {\left(a^{5} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{5} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 i \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, c^{3} f\right)} \sqrt{\frac{a^{11}}{c^{5} f^{2}}}}{a^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{5}}\right) - 315 \, {\left(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{3} f\right)} \sqrt{\frac{a^{11}}{c^{5} f^{2}}} \log\left(\frac{8 \, {\left(a^{5} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{5} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-4 i \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, c^{3} f\right)} \sqrt{\frac{a^{11}}{c^{5} f^{2}}}}{a^{5} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{5}}\right) + 2 \, {\left(-16 i \, a^{5} e^{\left(9 i \, f x + 9 i \, e\right)} + 48 i \, a^{5} e^{\left(7 i \, f x + 7 i \, e\right)} - 336 i \, a^{5} e^{\left(5 i \, f x + 5 i \, e\right)} - 1050 i \, a^{5} e^{\left(3 i \, f x + 3 i \, e\right)} - 630 i \, a^{5} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{20 \, {\left(c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + c^{3} f\right)}}"," ",0,"1/20*(315*(c^3*f*e^(2*I*f*x + 2*I*e) + c^3*f)*sqrt(a^11/(c^5*f^2))*log((8*(a^5*e^(3*I*f*x + 3*I*e) + a^5*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (4*I*c^3*f*e^(2*I*f*x + 2*I*e) - 4*I*c^3*f)*sqrt(a^11/(c^5*f^2)))/(a^5*e^(2*I*f*x + 2*I*e) + a^5)) - 315*(c^3*f*e^(2*I*f*x + 2*I*e) + c^3*f)*sqrt(a^11/(c^5*f^2))*log((8*(a^5*e^(3*I*f*x + 3*I*e) + a^5*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-4*I*c^3*f*e^(2*I*f*x + 2*I*e) + 4*I*c^3*f)*sqrt(a^11/(c^5*f^2)))/(a^5*e^(2*I*f*x + 2*I*e) + a^5)) + 2*(-16*I*a^5*e^(9*I*f*x + 9*I*e) + 48*I*a^5*e^(7*I*f*x + 7*I*e) - 336*I*a^5*e^(5*I*f*x + 5*I*e) - 1050*I*a^5*e^(3*I*f*x + 3*I*e) - 630*I*a^5*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c^3*f*e^(2*I*f*x + 2*I*e) + c^3*f)","A",0
1034,1,379,0,0.487954," ","integrate((a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{\frac{a^{9}}{c^{5} f^{2}}} c^{3} f \log\left(\frac{2 \, {\left(4 \, {\left(a^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{4} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c^{3} f\right)} \sqrt{\frac{a^{9}}{c^{5} f^{2}}}\right)}}{a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{4}}\right) - 105 \, \sqrt{\frac{a^{9}}{c^{5} f^{2}}} c^{3} f \log\left(\frac{2 \, {\left(4 \, {\left(a^{4} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{4} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c^{3} f\right)} \sqrt{\frac{a^{9}}{c^{5} f^{2}}}\right)}}{a^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{4}}\right) + {\left(-24 i \, a^{4} e^{\left(7 i \, f x + 7 i \, e\right)} + 56 i \, a^{4} e^{\left(5 i \, f x + 5 i \, e\right)} - 280 i \, a^{4} e^{\left(3 i \, f x + 3 i \, e\right)} - 420 i \, a^{4} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{30 \, c^{3} f}"," ",0,"1/30*(105*sqrt(a^9/(c^5*f^2))*c^3*f*log(2*(4*(a^4*e^(3*I*f*x + 3*I*e) + a^4*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*c^3*f*e^(2*I*f*x + 2*I*e) - 2*I*c^3*f)*sqrt(a^9/(c^5*f^2)))/(a^4*e^(2*I*f*x + 2*I*e) + a^4)) - 105*sqrt(a^9/(c^5*f^2))*c^3*f*log(2*(4*(a^4*e^(3*I*f*x + 3*I*e) + a^4*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*c^3*f*e^(2*I*f*x + 2*I*e) + 2*I*c^3*f)*sqrt(a^9/(c^5*f^2)))/(a^4*e^(2*I*f*x + 2*I*e) + a^4)) + (-24*I*a^4*e^(7*I*f*x + 7*I*e) + 56*I*a^4*e^(5*I*f*x + 5*I*e) - 280*I*a^4*e^(3*I*f*x + 3*I*e) - 420*I*a^4*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c^3*f)","B",0
1035,1,379,0,0.475791," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{15 \, c^{3} f \sqrt{\frac{a^{7}}{c^{5} f^{2}}} \log\left(\frac{2 \, {\left(4 \, {\left(a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(2 i \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c^{3} f\right)} \sqrt{\frac{a^{7}}{c^{5} f^{2}}}\right)}}{a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3}}\right) - 15 \, c^{3} f \sqrt{\frac{a^{7}}{c^{5} f^{2}}} \log\left(\frac{2 \, {\left(4 \, {\left(a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(-2 i \, c^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c^{3} f\right)} \sqrt{\frac{a^{7}}{c^{5} f^{2}}}\right)}}{a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3}}\right) + {\left(-12 i \, a^{3} e^{\left(7 i \, f x + 7 i \, e\right)} + 8 i \, a^{3} e^{\left(5 i \, f x + 5 i \, e\right)} - 40 i \, a^{3} e^{\left(3 i \, f x + 3 i \, e\right)} - 60 i \, a^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{30 \, c^{3} f}"," ",0,"1/30*(15*c^3*f*sqrt(a^7/(c^5*f^2))*log(2*(4*(a^3*e^(3*I*f*x + 3*I*e) + a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (2*I*c^3*f*e^(2*I*f*x + 2*I*e) - 2*I*c^3*f)*sqrt(a^7/(c^5*f^2)))/(a^3*e^(2*I*f*x + 2*I*e) + a^3)) - 15*c^3*f*sqrt(a^7/(c^5*f^2))*log(2*(4*(a^3*e^(3*I*f*x + 3*I*e) + a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)) + (-2*I*c^3*f*e^(2*I*f*x + 2*I*e) + 2*I*c^3*f)*sqrt(a^7/(c^5*f^2)))/(a^3*e^(2*I*f*x + 2*I*e) + a^3)) + (-12*I*a^3*e^(7*I*f*x + 7*I*e) + 8*I*a^3*e^(5*I*f*x + 5*I*e) - 40*I*a^3*e^(3*I*f*x + 3*I*e) - 60*I*a^3*e^(I*f*x + I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)))/(c^3*f)","B",0
1036,1,71,0,0.457011," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{2} e^{\left(7 i \, f x + 7 i \, e\right)} - i \, a^{2} e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{5 \, c^{3} f}"," ",0,"1/5*(-I*a^2*e^(7*I*f*x + 7*I*e) - I*a^2*e^(5*I*f*x + 5*I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","B",0
1037,1,79,0,0.426528," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-3 i \, a e^{\left(7 i \, f x + 7 i \, e\right)} - 8 i \, a e^{\left(5 i \, f x + 5 i \, e\right)} - 5 i \, a e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{30 \, c^{3} f}"," ",0,"1/30*(-3*I*a*e^(7*I*f*x + 7*I*e) - 8*I*a*e^(5*I*f*x + 5*I*e) - 5*I*a*e^(3*I*f*x + 3*I*e))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(c^3*f)","A",0
1038,1,87,0,0.478782," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-3 i \, e^{\left(7 i \, f x + 7 i \, e\right)} - 13 i \, e^{\left(5 i \, f x + 5 i \, e\right)} - 25 i \, e^{\left(3 i \, f x + 3 i \, e\right)} - 15 i \, e^{\left(i \, f x + i \, e\right)}\right)}}{60 \, c^{3} f}"," ",0,"1/60*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-3*I*e^(7*I*f*x + 7*I*e) - 13*I*e^(5*I*f*x + 5*I*e) - 25*I*e^(3*I*f*x + 3*I*e) - 15*I*e^(I*f*x + I*e))/(c^3*f)","A",0
1039,1,122,0,0.462284," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 6 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 20 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 16 i \, e^{\left(3 i \, f x + 3 i \, e\right)} - 10 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, e^{\left(i \, f x + i \, e\right)} + 5 i\right)} e^{\left(-i \, f x - i \, e\right)}}{40 \, a c^{3} f}"," ",0,"1/40*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(8*I*f*x + 8*I*e) - 6*I*e^(6*I*f*x + 6*I*e) - 20*I*e^(4*I*f*x + 4*I*e) + 16*I*e^(3*I*f*x + 3*I*e) - 10*I*e^(2*I*f*x + 2*I*e) + 16*I*e^(I*f*x + I*e) + 5*I)*e^(-I*f*x - I*e)/(a*c^3*f)","A",0
1040,1,133,0,0.445516," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-3 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 23 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 110 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 48 i \, e^{\left(5 i \, f x + 5 i \, e\right)} - 30 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 48 i \, e^{\left(3 i \, f x + 3 i \, e\right)} + 65 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 5 i\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{240 \, a^{2} c^{3} f}"," ",0,"1/240*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-3*I*e^(10*I*f*x + 10*I*e) - 23*I*e^(8*I*f*x + 8*I*e) - 110*I*e^(6*I*f*x + 6*I*e) + 48*I*e^(5*I*f*x + 5*I*e) - 30*I*e^(4*I*f*x + 4*I*e) + 48*I*e^(3*I*f*x + 3*I*e) + 65*I*e^(2*I*f*x + 2*I*e) + 5*I)*e^(-3*I*f*x - 3*I*e)/(a^2*c^3*f)","A",0
1041,1,111,0,0.435864," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-3 i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 28 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 175 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 175 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 28 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{480 \, a^{3} c^{3} f}"," ",0,"1/480*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-3*I*e^(12*I*f*x + 12*I*e) - 28*I*e^(10*I*f*x + 10*I*e) - 175*I*e^(8*I*f*x + 8*I*e) + 175*I*e^(4*I*f*x + 4*I*e) + 28*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(-5*I*f*x - 5*I*e)/(a^3*c^3*f)","A",0
1042,1,155,0,0.441969," ","integrate(1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-7 i \, e^{\left(14 i \, f x + 14 i \, e\right)} - 77 i \, e^{\left(12 i \, f x + 12 i \, e\right)} - 595 i \, e^{\left(10 i \, f x + 10 i \, e\right)} - 320 i \, e^{\left(9 i \, f x + 9 i \, e\right)} + 175 i \, e^{\left(8 i \, f x + 8 i \, e\right)} - 320 i \, e^{\left(7 i \, f x + 7 i \, e\right)} + 875 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 217 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 47 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 5 i\right)} e^{\left(-7 i \, f x - 7 i \, e\right)}}{2240 \, a^{4} c^{3} f}"," ",0,"1/2240*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(-7*I*e^(14*I*f*x + 14*I*e) - 77*I*e^(12*I*f*x + 12*I*e) - 595*I*e^(10*I*f*x + 10*I*e) - 320*I*e^(9*I*f*x + 9*I*e) + 175*I*e^(8*I*f*x + 8*I*e) - 320*I*e^(7*I*f*x + 7*I*e) + 875*I*e^(6*I*f*x + 6*I*e) + 217*I*e^(4*I*f*x + 4*I*e) + 47*I*e^(2*I*f*x + 2*I*e) + 5*I)*e^(-7*I*f*x - 7*I*e)/(a^4*c^3*f)","A",0
1043,1,237,0,0.452678," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left(48 i \, a^{4} + {\left(8 i \, a^{4} n^{3} + 48 i \, a^{4} n^{2} + 88 i \, a^{4} n + 48 i \, a^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(24 i \, a^{4} n^{2} + 120 i \, a^{4} n + 144 i \, a^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(48 i \, a^{4} n + 144 i \, a^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}}{f n^{4} + 6 \, f n^{3} + 11 \, f n^{2} + 6 \, f n + {\left(f n^{4} + 6 \, f n^{3} + 11 \, f n^{2} + 6 \, f n\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, {\left(f n^{4} + 6 \, f n^{3} + 11 \, f n^{2} + 6 \, f n\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, {\left(f n^{4} + 6 \, f n^{3} + 11 \, f n^{2} + 6 \, f n\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(48*I*a^4 + (8*I*a^4*n^3 + 48*I*a^4*n^2 + 88*I*a^4*n + 48*I*a^4)*e^(6*I*f*x + 6*I*e) + (24*I*a^4*n^2 + 120*I*a^4*n + 144*I*a^4)*e^(4*I*f*x + 4*I*e) + (48*I*a^4*n + 144*I*a^4)*e^(2*I*f*x + 2*I*e))*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n/(f*n^4 + 6*f*n^3 + 11*f*n^2 + 6*f*n + (f*n^4 + 6*f*n^3 + 11*f*n^2 + 6*f*n)*e^(6*I*f*x + 6*I*e) + 3*(f*n^4 + 6*f*n^3 + 11*f*n^2 + 6*f*n)*e^(4*I*f*x + 4*I*e) + 3*(f*n^4 + 6*f*n^3 + 11*f*n^2 + 6*f*n)*e^(2*I*f*x + 2*I*e))","B",0
1044,1,148,0,0.487190," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left(8 i \, a^{3} + {\left(4 i \, a^{3} n^{2} + 12 i \, a^{3} n + 8 i \, a^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(8 i \, a^{3} n + 16 i \, a^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}}{f n^{3} + 3 \, f n^{2} + 2 \, f n + {\left(f n^{3} + 3 \, f n^{2} + 2 \, f n\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(f n^{3} + 3 \, f n^{2} + 2 \, f n\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(8*I*a^3 + (4*I*a^3*n^2 + 12*I*a^3*n + 8*I*a^3)*e^(4*I*f*x + 4*I*e) + (8*I*a^3*n + 16*I*a^3)*e^(2*I*f*x + 2*I*e))*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n/(f*n^3 + 3*f*n^2 + 2*f*n + (f*n^3 + 3*f*n^2 + 2*f*n)*e^(4*I*f*x + 4*I*e) + 2*(f*n^3 + 3*f*n^2 + 2*f*n)*e^(2*I*f*x + 2*I*e))","A",0
1045,1,77,0,0.517588," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left(2 i \, a^{2} + {\left(2 i \, a^{2} n + 2 i \, a^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}}{f n^{2} + f n + {\left(f n^{2} + f n\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(2*I*a^2 + (2*I*a^2*n + 2*I*a^2)*e^(2*I*f*x + 2*I*e))*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n/(f*n^2 + f*n + (f*n^2 + f*n)*e^(2*I*f*x + 2*I*e))","A",0
1046,1,27,0,0.455480," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","\frac{i \, a \left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}}{f n}"," ",0,"I*a*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n/(f*n)","A",0
1047,0,0,0,0.430209," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(2*I*f*x + 2*I*e) + 1)*e^(-2*I*f*x - 2*I*e)/a, x)","F",0
1048,0,0,0,0.467153," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)*e^(-4*I*f*x - 4*I*e)/a^2, x)","F",0
1049,0,0,0,0.452867," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*(2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1)*e^(-6*I*f*x - 6*I*e)/a^3, x)","F",0
1050,0,0,0,0.464051," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(2 i \, f m x + 2 i \, e m + m \log\left(\frac{a}{c}\right) + m \log\left(\frac{2 \, c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)\right)}, x\right)"," ",0,"integral((2*c/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(2*I*f*m*x + 2*I*e*m + m*log(a/c) + m*log(2*c/(e^(2*I*f*x + 2*I*e) + 1))), x)","F",0
1051,1,244,0,0.451228," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(-8 i \, c^{4} m^{3} - 48 i \, c^{4} m^{2} - 88 i \, c^{4} m - 48 i \, c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} - 48 i \, c^{4} + {\left(-48 i \, c^{4} m - 144 i \, c^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-24 i \, c^{4} m^{2} - 120 i \, c^{4} m - 144 i \, c^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{f m^{4} + 6 \, f m^{3} + 11 \, f m^{2} + 6 \, f m + {\left(f m^{4} + 6 \, f m^{3} + 11 \, f m^{2} + 6 \, f m\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, {\left(f m^{4} + 6 \, f m^{3} + 11 \, f m^{2} + 6 \, f m\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, {\left(f m^{4} + 6 \, f m^{3} + 11 \, f m^{2} + 6 \, f m\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(-8*I*c^4*m^3 - 48*I*c^4*m^2 - 88*I*c^4*m - 48*I*c^4*e^(6*I*f*x + 6*I*e) - 48*I*c^4 + (-48*I*c^4*m - 144*I*c^4)*e^(4*I*f*x + 4*I*e) + (-24*I*c^4*m^2 - 120*I*c^4*m - 144*I*c^4)*e^(2*I*f*x + 2*I*e))*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(f*m^4 + 6*f*m^3 + 11*f*m^2 + 6*f*m + (f*m^4 + 6*f*m^3 + 11*f*m^2 + 6*f*m)*e^(6*I*f*x + 6*I*e) + 3*(f*m^4 + 6*f*m^3 + 11*f*m^2 + 6*f*m)*e^(4*I*f*x + 4*I*e) + 3*(f*m^4 + 6*f*m^3 + 11*f*m^2 + 6*f*m)*e^(2*I*f*x + 2*I*e))","B",0
1052,1,155,0,0.449983," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(-4 i \, c^{3} m^{2} - 12 i \, c^{3} m - 8 i \, c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 8 i \, c^{3} + {\left(-8 i \, c^{3} m - 16 i \, c^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{f m^{3} + 3 \, f m^{2} + 2 \, f m + {\left(f m^{3} + 3 \, f m^{2} + 2 \, f m\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(f m^{3} + 3 \, f m^{2} + 2 \, f m\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(-4*I*c^3*m^2 - 12*I*c^3*m - 8*I*c^3*e^(4*I*f*x + 4*I*e) - 8*I*c^3 + (-8*I*c^3*m - 16*I*c^3)*e^(2*I*f*x + 2*I*e))*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(f*m^3 + 3*f*m^2 + 2*f*m + (f*m^3 + 3*f*m^2 + 2*f*m)*e^(4*I*f*x + 4*I*e) + 2*(f*m^3 + 3*f*m^2 + 2*f*m)*e^(2*I*f*x + 2*I*e))","A",0
1053,1,84,0,0.477066," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-2 i \, c^{2} m - 2 i \, c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, c^{2}\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{f m^{2} + f m + {\left(f m^{2} + f m\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(-2*I*c^2*m - 2*I*c^2*e^(2*I*f*x + 2*I*e) - 2*I*c^2)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(f*m^2 + f*m + (f*m^2 + f*m)*e^(2*I*f*x + 2*I*e))","A",0
1054,1,36,0,0.531040," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{i \, c \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{f m}"," ",0,"-I*c*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(f*m)","A",0
1055,0,0,0,0.452365," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{2 \, c}, x\right)"," ",0,"integral(1/2*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(e^(2*I*f*x + 2*I*e) + 1)/c, x)","F",0
1056,0,0,0,0.483248," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{4 \, c^{2}}, x\right)"," ",0,"integral(1/4*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)/c^2, x)","F",0
1057,0,0,0,0.458072," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{8 \, c^{3}}, x\right)"," ",0,"integral(1/8*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1)/c^3, x)","F",0
1058,0,0,0,0.439203," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{16 \, c^{4}}, x\right)"," ",0,"integral(1/16*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(e^(8*I*f*x + 8*I*e) + 4*e^(6*I*f*x + 6*I*e) + 6*e^(4*I*f*x + 4*I*e) + 4*e^(2*I*f*x + 2*I*e) + 1)/c^4, x)","F",0
1059,0,0,0,0.452161," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, \sqrt{2} c^{2} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(4*sqrt(2)*c^2*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1060,0,0,0,0.478798," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \sqrt{2} c \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*sqrt(2)*c*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1061,0,0,0,0.437167," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}, x\right)"," ",0,"integral(sqrt(2)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1)), x)","F",0
1062,0,0,0,0.477885," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{2 \, c}, x\right)"," ",0,"integral(1/2*sqrt(2)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)/c, x)","F",0
1063,0,0,0,0.456694," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{4 \, c^{2}}, x\right)"," ",0,"integral(1/4*sqrt(2)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)/c^2, x)","F",0
1064,0,0,0,0.463569," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{c}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{8 \, c^{3}}, x\right)"," ",0,"integral(1/8*sqrt(2)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(c/(e^(2*I*f*x + 2*I*e) + 1))*(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1)/c^3, x)","F",0
1065,1,196,0,0.464098," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{-18 i \, a^{3} c - 26 \, a^{3} d - 24 \, {\left(i \, a^{3} c + 2 \, a^{3} d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} - 6 \, {\left(7 i \, a^{3} c + 11 \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - 12 \, {\left(i \, a^{3} c + a^{3} d + {\left(i \, a^{3} c + a^{3} d\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, {\left(i \, a^{3} c + a^{3} d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, {\left(i \, a^{3} c + a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-18*I*a^3*c - 26*a^3*d - 24*(I*a^3*c + 2*a^3*d)*e^(4*I*f*x + 4*I*e) - 6*(7*I*a^3*c + 11*a^3*d)*e^(2*I*f*x + 2*I*e) - 12*(I*a^3*c + a^3*d + (I*a^3*c + a^3*d)*e^(6*I*f*x + 6*I*e) + 3*(I*a^3*c + a^3*d)*e^(4*I*f*x + 4*I*e) + 3*(I*a^3*c + a^3*d)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1066,1,135,0,0.436416," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(i \, a^{2} c + 2 \, a^{2} d + {\left(i \, a^{2} c + 3 \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a^{2} c + a^{2} d + {\left(i \, a^{2} c + a^{2} d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(i \, a^{2} c + a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)\right)}}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"-2*(I*a^2*c + 2*a^2*d + (I*a^2*c + 3*a^2*d)*e^(2*I*f*x + 2*I*e) + (I*a^2*c + a^2*d + (I*a^2*c + a^2*d)*e^(4*I*f*x + 4*I*e) + 2*(I*a^2*c + a^2*d)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","A",0
1067,1,64,0,0.631611," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, a d - {\left(-i \, a c - a d + {\left(-i \, a c - a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"-(2*a*d - (-I*a*c - a*d + (-I*a*c - a*d)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(2*I*f*x + 2*I*e) + f)","A",0
1068,1,42,0,0.561495," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(c - i \, d\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*(2*(c - I*d)*f*x*e^(2*I*f*x + 2*I*e) + I*c - d)*e^(-2*I*f*x - 2*I*e)/(a*f)","A",0
1069,1,54,0,0.457467," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(c - i \, d\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + 4 i \, c e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"1/16*(4*(c - I*d)*f*x*e^(4*I*f*x + 4*I*e) + 4*I*c*e^(2*I*f*x + 2*I*e) + I*c - d)*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
1070,1,76,0,0.468018," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, {\left(c - i \, d\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(18 i \, c + 6 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 i \, c - 3 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c - 2 \, d\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} f}"," ",0,"1/96*(12*(c - I*d)*f*x*e^(6*I*f*x + 6*I*e) + (18*I*c + 6*d)*e^(4*I*f*x + 4*I*e) + (9*I*c - 3*d)*e^(2*I*f*x + 2*I*e) + 2*I*c - 2*d)*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
1071,1,352,0,0.429581," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-18 i \, a^{3} c^{2} - 52 \, a^{3} c d + 30 i \, a^{3} d^{2} + {\left(-24 i \, a^{3} c^{2} - 96 \, a^{3} c d + 72 i \, a^{3} d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-66 i \, a^{3} c^{2} - 228 \, a^{3} c d + 138 i \, a^{3} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-60 i \, a^{3} c^{2} - 184 \, a^{3} c d + 108 i \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-12 i \, a^{3} c^{2} - 24 \, a^{3} c d + 12 i \, a^{3} d^{2} + {\left(-12 i \, a^{3} c^{2} - 24 \, a^{3} c d + 12 i \, a^{3} d^{2}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-48 i \, a^{3} c^{2} - 96 \, a^{3} c d + 48 i \, a^{3} d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-72 i \, a^{3} c^{2} - 144 \, a^{3} c d + 72 i \, a^{3} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-48 i \, a^{3} c^{2} - 96 \, a^{3} c d + 48 i \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-18*I*a^3*c^2 - 52*a^3*c*d + 30*I*a^3*d^2 + (-24*I*a^3*c^2 - 96*a^3*c*d + 72*I*a^3*d^2)*e^(6*I*f*x + 6*I*e) + (-66*I*a^3*c^2 - 228*a^3*c*d + 138*I*a^3*d^2)*e^(4*I*f*x + 4*I*e) + (-60*I*a^3*c^2 - 184*a^3*c*d + 108*I*a^3*d^2)*e^(2*I*f*x + 2*I*e) + (-12*I*a^3*c^2 - 24*a^3*c*d + 12*I*a^3*d^2 + (-12*I*a^3*c^2 - 24*a^3*c*d + 12*I*a^3*d^2)*e^(8*I*f*x + 8*I*e) + (-48*I*a^3*c^2 - 96*a^3*c*d + 48*I*a^3*d^2)*e^(6*I*f*x + 6*I*e) + (-72*I*a^3*c^2 - 144*a^3*c*d + 72*I*a^3*d^2)*e^(4*I*f*x + 4*I*e) + (-48*I*a^3*c^2 - 96*a^3*c*d + 48*I*a^3*d^2)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1072,1,272,0,0.451597," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-6 i \, a^{2} c^{2} - 24 \, a^{2} c d + 14 i \, a^{2} d^{2} + {\left(-6 i \, a^{2} c^{2} - 36 \, a^{2} c d + 30 i \, a^{2} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-12 i \, a^{2} c^{2} - 60 \, a^{2} c d + 36 i \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, a^{2} c^{2} - 12 \, a^{2} c d + 6 i \, a^{2} d^{2} + {\left(-6 i \, a^{2} c^{2} - 12 \, a^{2} c d + 6 i \, a^{2} d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-18 i \, a^{2} c^{2} - 36 \, a^{2} c d + 18 i \, a^{2} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-18 i \, a^{2} c^{2} - 36 \, a^{2} c d + 18 i \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-6*I*a^2*c^2 - 24*a^2*c*d + 14*I*a^2*d^2 + (-6*I*a^2*c^2 - 36*a^2*c*d + 30*I*a^2*d^2)*e^(4*I*f*x + 4*I*e) + (-12*I*a^2*c^2 - 60*a^2*c*d + 36*I*a^2*d^2)*e^(2*I*f*x + 2*I*e) + (-6*I*a^2*c^2 - 12*a^2*c*d + 6*I*a^2*d^2 + (-6*I*a^2*c^2 - 12*a^2*c*d + 6*I*a^2*d^2)*e^(6*I*f*x + 6*I*e) + (-18*I*a^2*c^2 - 36*a^2*c*d + 18*I*a^2*d^2)*e^(4*I*f*x + 4*I*e) + (-18*I*a^2*c^2 - 36*a^2*c*d + 18*I*a^2*d^2)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1073,1,151,0,0.444509," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{4 \, a c d - 2 i \, a d^{2} + {\left(4 \, a c d - 4 i \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(-i \, a c^{2} - 2 \, a c d + i \, a d^{2} + {\left(-i \, a c^{2} - 2 \, a c d + i \, a d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-2 i \, a c^{2} - 4 \, a c d + 2 i \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"-(4*a*c*d - 2*I*a*d^2 + (4*a*c*d - 4*I*a*d^2)*e^(2*I*f*x + 2*I*e) - (-I*a*c^2 - 2*a*c*d + I*a*d^2 + (-I*a*c^2 - 2*a*c*d + I*a*d^2)*e^(4*I*f*x + 4*I*e) + (-2*I*a*c^2 - 4*a*c*d + 2*I*a*d^2)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1074,1,85,0,0.429023," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, c^{2} - 4 i \, c d + 6 \, d^{2}\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + i \, c^{2} - 2 \, c d - i \, d^{2}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a f}"," ",0,"1/4*((2*c^2 - 4*I*c*d + 6*d^2)*f*x*e^(2*I*f*x + 2*I*e) + 4*I*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + I*c^2 - 2*c*d - I*d^2)*e^(-2*I*f*x - 2*I*e)/(a*f)","A",0
1075,1,80,0,0.417760," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left(4 \, c^{2} - 8 i \, c d - 4 \, d^{2}\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + i \, c^{2} - 2 \, c d - i \, d^{2} + {\left(4 i \, c^{2} + 4 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"1/16*((4*c^2 - 8*I*c*d - 4*d^2)*f*x*e^(4*I*f*x + 4*I*e) + I*c^2 - 2*c*d - I*d^2 + (4*I*c^2 + 4*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
1076,1,109,0,0.440520," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(12 \, c^{2} - 24 i \, c d - 12 \, d^{2}\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + 2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + {\left(18 i \, c^{2} + 12 \, c d + 6 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 i \, c^{2} - 6 \, c d + 3 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} f}"," ",0,"1/96*((12*c^2 - 24*I*c*d - 12*d^2)*f*x*e^(6*I*f*x + 6*I*e) + 2*I*c^2 - 4*c*d - 2*I*d^2 + (18*I*c^2 + 12*c*d + 6*I*d^2)*e^(4*I*f*x + 4*I*e) + (9*I*c^2 - 6*c*d + 3*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
1077,1,553,0,0.519240," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-90 i \, a^{3} c^{3} - 390 \, a^{3} c^{2} d + 450 i \, a^{3} c d^{2} + 166 \, a^{3} d^{3} + {\left(-120 i \, a^{3} c^{3} - 720 \, a^{3} c^{2} d + 1080 i \, a^{3} c d^{2} + 480 \, a^{3} d^{3}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-450 i \, a^{3} c^{3} - 2430 \, a^{3} c^{2} d + 3150 i \, a^{3} c d^{2} + 1170 \, a^{3} d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-630 i \, a^{3} c^{3} - 3090 \, a^{3} c^{2} d + 3690 i \, a^{3} c d^{2} + 1390 \, a^{3} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-390 i \, a^{3} c^{3} - 1770 \, a^{3} c^{2} d + 2070 i \, a^{3} c d^{2} + 770 \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-60 i \, a^{3} c^{3} - 180 \, a^{3} c^{2} d + 180 i \, a^{3} c d^{2} + 60 \, a^{3} d^{3} + {\left(-60 i \, a^{3} c^{3} - 180 \, a^{3} c^{2} d + 180 i \, a^{3} c d^{2} + 60 \, a^{3} d^{3}\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-300 i \, a^{3} c^{3} - 900 \, a^{3} c^{2} d + 900 i \, a^{3} c d^{2} + 300 \, a^{3} d^{3}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-600 i \, a^{3} c^{3} - 1800 \, a^{3} c^{2} d + 1800 i \, a^{3} c d^{2} + 600 \, a^{3} d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-600 i \, a^{3} c^{3} - 1800 \, a^{3} c^{2} d + 1800 i \, a^{3} c d^{2} + 600 \, a^{3} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-300 i \, a^{3} c^{3} - 900 \, a^{3} c^{2} d + 900 i \, a^{3} c d^{2} + 300 \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{15 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(-90*I*a^3*c^3 - 390*a^3*c^2*d + 450*I*a^3*c*d^2 + 166*a^3*d^3 + (-120*I*a^3*c^3 - 720*a^3*c^2*d + 1080*I*a^3*c*d^2 + 480*a^3*d^3)*e^(8*I*f*x + 8*I*e) + (-450*I*a^3*c^3 - 2430*a^3*c^2*d + 3150*I*a^3*c*d^2 + 1170*a^3*d^3)*e^(6*I*f*x + 6*I*e) + (-630*I*a^3*c^3 - 3090*a^3*c^2*d + 3690*I*a^3*c*d^2 + 1390*a^3*d^3)*e^(4*I*f*x + 4*I*e) + (-390*I*a^3*c^3 - 1770*a^3*c^2*d + 2070*I*a^3*c*d^2 + 770*a^3*d^3)*e^(2*I*f*x + 2*I*e) + (-60*I*a^3*c^3 - 180*a^3*c^2*d + 180*I*a^3*c*d^2 + 60*a^3*d^3 + (-60*I*a^3*c^3 - 180*a^3*c^2*d + 180*I*a^3*c*d^2 + 60*a^3*d^3)*e^(10*I*f*x + 10*I*e) + (-300*I*a^3*c^3 - 900*a^3*c^2*d + 900*I*a^3*c*d^2 + 300*a^3*d^3)*e^(8*I*f*x + 8*I*e) + (-600*I*a^3*c^3 - 1800*a^3*c^2*d + 1800*I*a^3*c*d^2 + 600*a^3*d^3)*e^(6*I*f*x + 6*I*e) + (-600*I*a^3*c^3 - 1800*a^3*c^2*d + 1800*I*a^3*c*d^2 + 600*a^3*d^3)*e^(4*I*f*x + 4*I*e) + (-300*I*a^3*c^3 - 900*a^3*c^2*d + 900*I*a^3*c*d^2 + 300*a^3*d^3)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1078,1,451,0,0.473741," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{-6 i \, a^{2} c^{3} - 36 \, a^{2} c^{2} d + 42 i \, a^{2} c d^{2} + 16 \, a^{2} d^{3} + {\left(-6 i \, a^{2} c^{3} - 54 \, a^{2} c^{2} d + 90 i \, a^{2} c d^{2} + 42 \, a^{2} d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-18 i \, a^{2} c^{3} - 144 \, a^{2} c^{2} d + 198 i \, a^{2} c d^{2} + 72 \, a^{2} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-18 i \, a^{2} c^{3} - 126 \, a^{2} c^{2} d + 150 i \, a^{2} c d^{2} + 58 \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, a^{2} c^{3} - 18 \, a^{2} c^{2} d + 18 i \, a^{2} c d^{2} + 6 \, a^{2} d^{3} + {\left(-6 i \, a^{2} c^{3} - 18 \, a^{2} c^{2} d + 18 i \, a^{2} c d^{2} + 6 \, a^{2} d^{3}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-24 i \, a^{2} c^{3} - 72 \, a^{2} c^{2} d + 72 i \, a^{2} c d^{2} + 24 \, a^{2} d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-36 i \, a^{2} c^{3} - 108 \, a^{2} c^{2} d + 108 i \, a^{2} c d^{2} + 36 \, a^{2} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-24 i \, a^{2} c^{3} - 72 \, a^{2} c^{2} d + 72 i \, a^{2} c d^{2} + 24 \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-6*I*a^2*c^3 - 36*a^2*c^2*d + 42*I*a^2*c*d^2 + 16*a^2*d^3 + (-6*I*a^2*c^3 - 54*a^2*c^2*d + 90*I*a^2*c*d^2 + 42*a^2*d^3)*e^(6*I*f*x + 6*I*e) + (-18*I*a^2*c^3 - 144*a^2*c^2*d + 198*I*a^2*c*d^2 + 72*a^2*d^3)*e^(4*I*f*x + 4*I*e) + (-18*I*a^2*c^3 - 126*a^2*c^2*d + 150*I*a^2*c*d^2 + 58*a^2*d^3)*e^(2*I*f*x + 2*I*e) + (-6*I*a^2*c^3 - 18*a^2*c^2*d + 18*I*a^2*c*d^2 + 6*a^2*d^3 + (-6*I*a^2*c^3 - 18*a^2*c^2*d + 18*I*a^2*c*d^2 + 6*a^2*d^3)*e^(8*I*f*x + 8*I*e) + (-24*I*a^2*c^3 - 72*a^2*c^2*d + 72*I*a^2*c*d^2 + 24*a^2*d^3)*e^(6*I*f*x + 6*I*e) + (-36*I*a^2*c^3 - 108*a^2*c^2*d + 108*I*a^2*c*d^2 + 36*a^2*d^3)*e^(4*I*f*x + 4*I*e) + (-24*I*a^2*c^3 - 72*a^2*c^2*d + 72*I*a^2*c*d^2 + 24*a^2*d^3)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1079,1,276,0,0.483618," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{18 \, a c^{2} d - 18 i \, a c d^{2} - 8 \, a d^{3} + {\left(18 \, a c^{2} d - 36 i \, a c d^{2} - 18 \, a d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(36 \, a c^{2} d - 54 i \, a c d^{2} - 18 \, a d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(-3 i \, a c^{3} - 9 \, a c^{2} d + 9 i \, a c d^{2} + 3 \, a d^{3} + {\left(-3 i \, a c^{3} - 9 \, a c^{2} d + 9 i \, a c d^{2} + 3 \, a d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-9 i \, a c^{3} - 27 \, a c^{2} d + 27 i \, a c d^{2} + 9 \, a d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-9 i \, a c^{3} - 27 \, a c^{2} d + 27 i \, a c d^{2} + 9 \, a d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/3*(18*a*c^2*d - 18*I*a*c*d^2 - 8*a*d^3 + (18*a*c^2*d - 36*I*a*c*d^2 - 18*a*d^3)*e^(4*I*f*x + 4*I*e) + (36*a*c^2*d - 54*I*a*c*d^2 - 18*a*d^3)*e^(2*I*f*x + 2*I*e) - (-3*I*a*c^3 - 9*a*c^2*d + 9*I*a*c*d^2 + 3*a*d^3 + (-3*I*a*c^3 - 9*a*c^2*d + 9*I*a*c*d^2 + 3*a*d^3)*e^(6*I*f*x + 6*I*e) + (-9*I*a*c^3 - 27*a*c^2*d + 27*I*a*c*d^2 + 9*a*d^3)*e^(4*I*f*x + 4*I*e) + (-9*I*a*c^3 - 27*a*c^2*d + 27*I*a*c*d^2 + 9*a*d^3)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1080,1,202,0,0.509191," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, c^{3} - 6 i \, c^{2} d + 18 \, c d^{2} + 10 i \, d^{3}\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + i \, c^{3} - 3 \, c^{2} d - 3 i \, c d^{2} + d^{3} + {\left(i \, c^{3} - 3 \, c^{2} d - 3 i \, c d^{2} + 9 \, d^{3} + {\left(2 \, c^{3} - 6 i \, c^{2} d + 18 \, c d^{2} + 10 i \, d^{3}\right)} f x\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left({\left(12 i \, c d^{2} - 4 \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(12 i \, c d^{2} - 4 \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{4 \, {\left(a f e^{\left(4 i \, f x + 4 i \, e\right)} + a f e^{\left(2 i \, f x + 2 i \, e\right)}\right)}}"," ",0,"1/4*((2*c^3 - 6*I*c^2*d + 18*c*d^2 + 10*I*d^3)*f*x*e^(4*I*f*x + 4*I*e) + I*c^3 - 3*c^2*d - 3*I*c*d^2 + d^3 + (I*c^3 - 3*c^2*d - 3*I*c*d^2 + 9*d^3 + (2*c^3 - 6*I*c^2*d + 18*c*d^2 + 10*I*d^3)*f*x)*e^(2*I*f*x + 2*I*e) + ((12*I*c*d^2 - 4*d^3)*e^(4*I*f*x + 4*I*e) + (12*I*c*d^2 - 4*d^3)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/(a*f*e^(4*I*f*x + 4*I*e) + a*f*e^(2*I*f*x + 2*I*e))","A",0
1081,1,126,0,0.524246," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(16 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + {\left(4 \, c^{3} - 12 i \, c^{2} d - 12 \, c d^{2} - 28 i \, d^{3}\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + i \, c^{3} - 3 \, c^{2} d - 3 i \, c d^{2} + d^{3} + {\left(4 i \, c^{3} + 12 i \, c d^{2} - 8 \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, a^{2} f}"," ",0,"1/16*(16*d^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + (4*c^3 - 12*I*c^2*d - 12*c*d^2 - 28*I*d^3)*f*x*e^(4*I*f*x + 4*I*e) + I*c^3 - 3*c^2*d - 3*I*c*d^2 + d^3 + (4*I*c^3 + 12*I*c*d^2 - 8*d^3)*e^(2*I*f*x + 2*I*e))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
1082,1,141,0,0.418990," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(12 \, c^{3} - 36 i \, c^{2} d - 36 \, c d^{2} + 12 i \, d^{3}\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + 2 i \, c^{3} - 6 \, c^{2} d - 6 i \, c d^{2} + 2 \, d^{3} + {\left(18 i \, c^{3} + 18 \, c^{2} d + 18 i \, c d^{2} + 18 \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 i \, c^{3} - 9 \, c^{2} d + 9 i \, c d^{2} - 9 \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, a^{3} f}"," ",0,"1/96*((12*c^3 - 36*I*c^2*d - 36*c*d^2 + 12*I*d^3)*f*x*e^(6*I*f*x + 6*I*e) + 2*I*c^3 - 6*c^2*d - 6*I*c*d^2 + 2*d^3 + (18*I*c^3 + 18*c^2*d + 18*I*c*d^2 + 18*d^3)*e^(4*I*f*x + 4*I*e) + (9*I*c^3 - 9*c^2*d + 9*I*c*d^2 - 9*d^3)*e^(2*I*f*x + 2*I*e))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
1083,1,211,0,0.483619," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 i \, a^{3} c d + 2 \, a^{3} d^{2} - {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2} + {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right) + {\left(a^{3} c^{2} + 2 i \, a^{3} c d + 3 \, a^{3} d^{2} + {\left(a^{3} c^{2} + 2 i \, a^{3} c d + 3 \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{{\left(i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c d^{2} + d^{3}\right)} f}"," ",0,"(2*I*a^3*c*d + 2*a^3*d^2 - (a^3*c^2 + 2*I*a^3*c*d - a^3*d^2 + (a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)) + (a^3*c^2 + 2*I*a^3*c*d + 3*a^3*d^2 + (a^3*c^2 + 2*I*a^3*c*d + 3*a^3*d^2)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/((I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (I*c*d^2 + d^3)*f)","A",0
1084,1,84,0,0.474924," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{2} c + a^{2} d\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right) + {\left(i \, a^{2} c + a^{2} d\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{{\left(i \, c d + d^{2}\right)} f}"," ",0,"((-I*a^2*c + a^2*d)*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)) + (I*a^2*c + a^2*d)*log(e^(2*I*f*x + 2*I*e) + 1))/((I*c*d + d^2)*f)","A",0
1085,1,43,0,0.462717," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{a \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(i \, c + d\right)} f}"," ",0,"a*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d))/((I*c + d)*f)","A",0
1086,1,121,0,0.478157," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left({\left(-2 i \, c^{2} + 4 \, c d - 6 i \, d^{2}\right)} f x e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right) + c^{2} + d^{2}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(-4 i \, a c^{3} + 4 \, a c^{2} d - 4 i \, a c d^{2} + 4 \, a d^{3}\right)} f}"," ",0,"((-2*I*c^2 + 4*c*d - 6*I*d^2)*f*x*e^(2*I*f*x + 2*I*e) + 4*d^2*e^(2*I*f*x + 2*I*e)*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)) + c^2 + d^2)*e^(-2*I*f*x - 2*I*e)/((-4*I*a*c^3 + 4*a*c^2*d - 4*I*a*c*d^2 + 4*a*d^3)*f)","A",0
1087,1,185,0,0.615627," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(16 \, d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right) - {\left(4 \, c^{3} + 12 i \, c^{2} d - 12 \, c d^{2} + 28 i \, d^{3}\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} - i \, c^{3} + c^{2} d - i \, c d^{2} + d^{3} + {\left(-4 i \, c^{3} + 8 \, c^{2} d - 4 i \, c d^{2} + 8 \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{{\left(16 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d + 32 i \, a^{2} c d^{3} - 16 \, a^{2} d^{4}\right)} f}"," ",0,"-(16*d^3*e^(4*I*f*x + 4*I*e)*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)) - (4*c^3 + 12*I*c^2*d - 12*c*d^2 + 28*I*d^3)*f*x*e^(4*I*f*x + 4*I*e) - I*c^3 + c^2*d - I*c*d^2 + d^3 + (-4*I*c^3 + 8*c^2*d - 4*I*c*d^2 + 8*d^3)*e^(2*I*f*x + 2*I*e))*e^(-4*I*f*x - 4*I*e)/((16*a^2*c^4 + 32*I*a^2*c^3*d + 32*I*a^2*c*d^3 - 16*a^2*d^4)*f)","A",0
1088,1,267,0,0.509167," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(96 \, d^{4} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right) - 2 \, c^{4} - 4 i \, c^{3} d - 4 i \, c d^{3} + 2 \, d^{4} + {\left(12 i \, c^{4} - 48 \, c^{3} d - 72 i \, c^{2} d^{2} + 48 \, c d^{3} - 180 i \, d^{4}\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} - {\left(18 \, c^{4} + 60 i \, c^{3} d - 48 \, c^{2} d^{2} + 60 i \, c d^{3} - 66 \, d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} - {\left(9 \, c^{4} + 24 i \, c^{3} d - 6 \, c^{2} d^{2} + 24 i \, c d^{3} - 15 \, d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{{\left(96 i \, a^{3} c^{5} - 288 \, a^{3} c^{4} d - 192 i \, a^{3} c^{3} d^{2} - 192 \, a^{3} c^{2} d^{3} - 288 i \, a^{3} c d^{4} + 96 \, a^{3} d^{5}\right)} f}"," ",0,"(96*d^4*e^(6*I*f*x + 6*I*e)*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)) - 2*c^4 - 4*I*c^3*d - 4*I*c*d^3 + 2*d^4 + (12*I*c^4 - 48*c^3*d - 72*I*c^2*d^2 + 48*c*d^3 - 180*I*d^4)*f*x*e^(6*I*f*x + 6*I*e) - (18*c^4 + 60*I*c^3*d - 48*c^2*d^2 + 60*I*c*d^3 - 66*d^4)*e^(4*I*f*x + 4*I*e) - (9*c^4 + 24*I*c^3*d - 6*c^2*d^2 + 24*I*c*d^3 - 15*d^4)*e^(2*I*f*x + 2*I*e))*e^(-6*I*f*x - 6*I*e)/((96*I*a^3*c^5 - 288*a^3*c^4*d - 192*I*a^3*c^3*d^2 - 192*a^3*c^2*d^3 - 288*I*a^3*c*d^4 + 96*a^3*d^5)*f)","A",0
1089,1,298,0,0.640091," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 i \, a^{3} c^{2} d - 4 \, a^{3} c d^{2} - 2 i \, a^{3} d^{3} - {\left(a^{3} c^{3} - i \, a^{3} c^{2} d + 5 \, a^{3} c d^{2} + 3 i \, a^{3} d^{3} + {\left(a^{3} c^{3} - 3 i \, a^{3} c^{2} d + a^{3} c d^{2} - 3 i \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right) + {\left(a^{3} c^{3} - i \, a^{3} c^{2} d + a^{3} c d^{2} - i \, a^{3} d^{3} + {\left(a^{3} c^{3} - 3 i \, a^{3} c^{2} d - 3 \, a^{3} c d^{2} + i \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}{{\left(-i \, c^{3} d^{2} - 3 \, c^{2} d^{3} + 3 i \, c d^{4} + d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} d^{2} - c^{2} d^{3} - i \, c d^{4} - d^{5}\right)} f}"," ",0,"(2*I*a^3*c^2*d - 4*a^3*c*d^2 - 2*I*a^3*d^3 - (a^3*c^3 - I*a^3*c^2*d + 5*a^3*c*d^2 + 3*I*a^3*d^3 + (a^3*c^3 - 3*I*a^3*c^2*d + a^3*c*d^2 - 3*I*a^3*d^3)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)) + (a^3*c^3 - I*a^3*c^2*d + a^3*c*d^2 - I*a^3*d^3 + (a^3*c^3 - 3*I*a^3*c^2*d - 3*a^3*c*d^2 + I*a^3*d^3)*e^(2*I*f*x + 2*I*e))*log(e^(2*I*f*x + 2*I*e) + 1))/((-I*c^3*d^2 - 3*c^2*d^3 + 3*I*c*d^4 + d^5)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3*d^2 - c^2*d^3 - I*c*d^4 - d^5)*f)","B",0
1090,1,143,0,0.488797," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} c + 2 i \, a^{2} d + {\left(2 \, a^{2} c + 2 i \, a^{2} d + {\left(2 \, a^{2} c - 2 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} - c^{2} d - i \, c d^{2} - d^{3}\right)} f}"," ",0,"-(2*a^2*c + 2*I*a^2*d + (2*a^2*c + 2*I*a^2*d + (2*a^2*c - 2*I*a^2*d)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3 - c^2*d - I*c*d^2 - d^3)*f)","A",0
1091,1,125,0,0.456382," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, a d - {\left(a c + i \, a d + {\left(a c - i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} - c^{2} d - i \, c d^{2} - d^{3}\right)} f}"," ",0,"(-2*I*a*d - (a*c + I*a*d + (a*c - I*a*d)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3 - c^2*d - I*c*d^2 - d^3)*f)","A",0
1092,1,332,0,0.511492," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{i \, c^{4} + 2 i \, c^{2} d^{2} + i \, d^{4} + {\left(2 \, c^{4} + 4 i \, c^{3} d + 24 \, c^{2} d^{2} - 28 i \, c d^{3} - 10 \, d^{4}\right)} f x e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(i \, c^{4} + 2 \, c^{3} d - 6 \, c d^{3} - 9 i \, d^{4} + {\left(2 \, c^{4} + 8 i \, c^{3} d + 12 \, c^{2} d^{2} + 8 i \, c d^{3} + 10 \, d^{4}\right)} f x\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left({\left(12 i \, c^{2} d^{2} + 16 \, c d^{3} - 4 i \, d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(12 i \, c^{2} d^{2} - 8 \, c d^{3} + 4 i \, d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{4 \, {\left(a c^{6} + 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} + a d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 \, a c^{6} + 8 i \, a c^{5} d + 4 \, a c^{4} d^{2} + 16 i \, a c^{3} d^{3} - 4 \, a c^{2} d^{4} + 8 i \, a c d^{5} - 4 \, a d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(I*c^4 + 2*I*c^2*d^2 + I*d^4 + (2*c^4 + 4*I*c^3*d + 24*c^2*d^2 - 28*I*c*d^3 - 10*d^4)*f*x*e^(4*I*f*x + 4*I*e) + (I*c^4 + 2*c^3*d - 6*c*d^3 - 9*I*d^4 + (2*c^4 + 8*I*c^3*d + 12*c^2*d^2 + 8*I*c*d^3 + 10*d^4)*f*x)*e^(2*I*f*x + 2*I*e) + ((12*I*c^2*d^2 + 16*c*d^3 - 4*I*d^4)*e^(4*I*f*x + 4*I*e) + (12*I*c^2*d^2 - 8*c*d^3 + 4*I*d^4)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/(4*(a*c^6 + 3*a*c^4*d^2 + 3*a*c^2*d^4 + a*d^6)*f*e^(4*I*f*x + 4*I*e) + (4*a*c^6 + 8*I*a*c^5*d + 4*a*c^4*d^2 + 16*I*a*c^3*d^3 - 4*a*c^2*d^4 + 8*I*a*c*d^5 - 4*a*d^6)*f*e^(2*I*f*x + 2*I*e))","A",0
1093,1,504,0,0.504888," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{c^{5} + i \, c^{4} d + 2 \, c^{3} d^{2} + 2 i \, c^{2} d^{3} + c d^{4} + i \, d^{5} + {\left(-4 i \, c^{5} + 12 \, c^{4} d + 8 i \, c^{3} d^{2} + 136 \, c^{2} d^{3} - 180 i \, c d^{4} - 68 \, d^{5}\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(4 \, c^{5} + 4 i \, c^{4} d + 24 \, c^{3} d^{2} - 8 i \, c^{2} d^{3} - 12 \, c d^{4} - 44 i \, d^{5} + {\left(-4 i \, c^{5} + 20 \, c^{4} d + 40 i \, c^{3} d^{2} + 88 \, c^{2} d^{3} + 44 i \, c d^{4} + 68 \, d^{5}\right)} f x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(5 \, c^{5} + 11 i \, c^{4} d + 10 \, c^{3} d^{2} + 22 i \, c^{2} d^{3} + 5 \, c d^{4} + 11 i \, d^{5}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left({\left(64 i \, c^{2} d^{3} + 96 \, c d^{4} - 32 i \, d^{5}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(64 i \, c^{2} d^{3} - 32 \, c d^{4} + 32 i \, d^{5}\right)} e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(-16 i \, a^{2} c^{7} + 16 \, a^{2} c^{6} d - 48 i \, a^{2} c^{5} d^{2} + 48 \, a^{2} c^{4} d^{3} - 48 i \, a^{2} c^{3} d^{4} + 48 \, a^{2} c^{2} d^{5} - 16 i \, a^{2} c d^{6} + 16 \, a^{2} d^{7}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-16 i \, a^{2} c^{7} + 48 \, a^{2} c^{6} d + 16 i \, a^{2} c^{5} d^{2} + 80 \, a^{2} c^{4} d^{3} + 80 i \, a^{2} c^{3} d^{4} + 16 \, a^{2} c^{2} d^{5} + 48 i \, a^{2} c d^{6} - 16 \, a^{2} d^{7}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}}"," ",0,"(c^5 + I*c^4*d + 2*c^3*d^2 + 2*I*c^2*d^3 + c*d^4 + I*d^5 + (-4*I*c^5 + 12*c^4*d + 8*I*c^3*d^2 + 136*c^2*d^3 - 180*I*c*d^4 - 68*d^5)*f*x*e^(6*I*f*x + 6*I*e) + (4*c^5 + 4*I*c^4*d + 24*c^3*d^2 - 8*I*c^2*d^3 - 12*c*d^4 - 44*I*d^5 + (-4*I*c^5 + 20*c^4*d + 40*I*c^3*d^2 + 88*c^2*d^3 + 44*I*c*d^4 + 68*d^5)*f*x)*e^(4*I*f*x + 4*I*e) + (5*c^5 + 11*I*c^4*d + 10*c^3*d^2 + 22*I*c^2*d^3 + 5*c*d^4 + 11*I*d^5)*e^(2*I*f*x + 2*I*e) + ((64*I*c^2*d^3 + 96*c*d^4 - 32*I*d^5)*e^(6*I*f*x + 6*I*e) + (64*I*c^2*d^3 - 32*c*d^4 + 32*I*d^5)*e^(4*I*f*x + 4*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((-16*I*a^2*c^7 + 16*a^2*c^6*d - 48*I*a^2*c^5*d^2 + 48*a^2*c^4*d^3 - 48*I*a^2*c^3*d^4 + 48*a^2*c^2*d^5 - 16*I*a^2*c*d^6 + 16*a^2*d^7)*f*e^(6*I*f*x + 6*I*e) + (-16*I*a^2*c^7 + 48*a^2*c^6*d + 16*I*a^2*c^5*d^2 + 80*a^2*c^4*d^3 + 80*I*a^2*c^3*d^4 + 16*a^2*c^2*d^5 + 48*I*a^2*c*d^6 - 16*a^2*d^7)*f*e^(4*I*f*x + 4*I*e))","B",0
1094,1,604,0,0.468531," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{-2 i \, c^{6} + 4 \, c^{5} d - 2 i \, c^{4} d^{2} + 8 \, c^{3} d^{3} + 2 i \, c^{2} d^{4} + 4 \, c d^{5} + 2 i \, d^{6} - {\left(12 \, c^{6} + 48 i \, c^{5} d - 60 \, c^{4} d^{2} - 1020 \, c^{2} d^{4} + 1488 i \, c d^{5} + 588 \, d^{6}\right)} f x e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-18 i \, c^{6} + 48 \, c^{5} d - 30 i \, c^{4} d^{2} + 240 \, c^{3} d^{3} - 150 i \, c^{2} d^{4} - 330 i \, d^{6} - {\left(12 \, c^{6} + 72 i \, c^{5} d - 180 \, c^{4} d^{2} - 240 i \, c^{3} d^{3} - 780 \, c^{2} d^{4} - 312 i \, c d^{5} - 588 \, d^{6}\right)} f x\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-27 i \, c^{6} + 96 \, c^{5} d + 63 i \, c^{4} d^{2} + 192 \, c^{3} d^{3} + 207 i \, c^{2} d^{4} + 96 \, c d^{5} + 117 i \, d^{6}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-11 i \, c^{6} + 30 \, c^{5} d - 3 i \, c^{4} d^{2} + 60 \, c^{3} d^{3} + 27 i \, c^{2} d^{4} + 30 \, c d^{5} + 19 i \, d^{6}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left({\left(480 i \, c^{2} d^{4} + 768 \, c d^{5} - 288 i \, d^{6}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(480 i \, c^{2} d^{4} - 192 \, c d^{5} + 288 i \, d^{6}\right)} e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(96 \, a^{3} c^{8} + 192 i \, a^{3} c^{7} d + 192 \, a^{3} c^{6} d^{2} + 576 i \, a^{3} c^{5} d^{3} + 576 i \, a^{3} c^{3} d^{5} - 192 \, a^{3} c^{2} d^{6} + 192 i \, a^{3} c d^{7} - 96 \, a^{3} d^{8}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(96 \, a^{3} c^{8} + 384 i \, a^{3} c^{7} d - 384 \, a^{3} c^{6} d^{2} + 384 i \, a^{3} c^{5} d^{3} - 960 \, a^{3} c^{4} d^{4} - 384 i \, a^{3} c^{3} d^{5} - 384 \, a^{3} c^{2} d^{6} - 384 i \, a^{3} c d^{7} + 96 \, a^{3} d^{8}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}}"," ",0,"-(-2*I*c^6 + 4*c^5*d - 2*I*c^4*d^2 + 8*c^3*d^3 + 2*I*c^2*d^4 + 4*c*d^5 + 2*I*d^6 - (12*c^6 + 48*I*c^5*d - 60*c^4*d^2 - 1020*c^2*d^4 + 1488*I*c*d^5 + 588*d^6)*f*x*e^(8*I*f*x + 8*I*e) + (-18*I*c^6 + 48*c^5*d - 30*I*c^4*d^2 + 240*c^3*d^3 - 150*I*c^2*d^4 - 330*I*d^6 - (12*c^6 + 72*I*c^5*d - 180*c^4*d^2 - 240*I*c^3*d^3 - 780*c^2*d^4 - 312*I*c*d^5 - 588*d^6)*f*x)*e^(6*I*f*x + 6*I*e) + (-27*I*c^6 + 96*c^5*d + 63*I*c^4*d^2 + 192*c^3*d^3 + 207*I*c^2*d^4 + 96*c*d^5 + 117*I*d^6)*e^(4*I*f*x + 4*I*e) + (-11*I*c^6 + 30*c^5*d - 3*I*c^4*d^2 + 60*c^3*d^3 + 27*I*c^2*d^4 + 30*c*d^5 + 19*I*d^6)*e^(2*I*f*x + 2*I*e) + ((480*I*c^2*d^4 + 768*c*d^5 - 288*I*d^6)*e^(8*I*f*x + 8*I*e) + (480*I*c^2*d^4 - 192*c*d^5 + 288*I*d^6)*e^(6*I*f*x + 6*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((96*a^3*c^8 + 192*I*a^3*c^7*d + 192*a^3*c^6*d^2 + 576*I*a^3*c^5*d^3 + 576*I*a^3*c^3*d^5 - 192*a^3*c^2*d^6 + 192*I*a^3*c*d^7 - 96*a^3*d^8)*f*e^(8*I*f*x + 8*I*e) + (96*a^3*c^8 + 384*I*a^3*c^7*d - 384*a^3*c^6*d^2 + 384*I*a^3*c^5*d^3 - 960*a^3*c^4*d^4 - 384*I*a^3*c^3*d^5 - 384*a^3*c^2*d^6 - 384*I*a^3*c*d^7 + 96*a^3*d^8)*f*e^(6*I*f*x + 6*I*e))","A",0
1095,1,306,0,0.425001," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{3} c^{2} + 6 i \, a^{3} c d - 3 \, a^{3} d^{2} + 4 \, {\left(a^{3} c^{2} + a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2} + {\left(a^{3} c^{2} - 2 i \, a^{3} c d - a^{3} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(a^{3} c^{2} + a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)\right)}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, c^{5} + 6 \, c^{4} d - 4 i \, c^{3} d^{2} + 4 \, c^{2} d^{3} - 6 i \, c d^{4} - 2 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{5} + c^{4} d + 2 i \, c^{3} d^{2} + 2 \, c^{2} d^{3} + i \, c d^{4} + d^{5}\right)} f}"," ",0,"2*(3*a^3*c^2 + 6*I*a^3*c*d - 3*a^3*d^2 + 4*(a^3*c^2 + a^3*d^2)*e^(2*I*f*x + 2*I*e) + 2*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2 + (a^3*c^2 - 2*I*a^3*c*d - a^3*d^2)*e^(4*I*f*x + 4*I*e) + 2*(a^3*c^2 + a^3*d^2)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f*e^(4*I*f*x + 4*I*e) + (2*I*c^5 + 6*c^4*d - 4*I*c^3*d^2 + 4*c^2*d^3 - 6*I*c*d^4 - 2*d^5)*f*e^(2*I*f*x + 2*I*e) + (I*c^5 + c^4*d + 2*I*c^3*d^2 + 2*c^2*d^3 + I*c*d^4 + d^5)*f)","B",0
1096,1,311,0,0.435520," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} c^{2} + 3 i \, a^{2} c d - 2 \, a^{2} d^{2} + {\left(a^{2} c^{2} + 2 i \, a^{2} c d + 3 \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2} + {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(a^{2} c^{2} + a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)\right)}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, c^{5} + 6 \, c^{4} d - 4 i \, c^{3} d^{2} + 4 \, c^{2} d^{3} - 6 i \, c d^{4} - 2 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{5} + c^{4} d + 2 i \, c^{3} d^{2} + 2 \, c^{2} d^{3} + i \, c d^{4} + d^{5}\right)} f}"," ",0,"2*(a^2*c^2 + 3*I*a^2*c*d - 2*a^2*d^2 + (a^2*c^2 + 2*I*a^2*c*d + 3*a^2*d^2)*e^(2*I*f*x + 2*I*e) + (a^2*c^2 + 2*I*a^2*c*d - a^2*d^2 + (a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)*e^(4*I*f*x + 4*I*e) + 2*(a^2*c^2 + a^2*d^2)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f*e^(4*I*f*x + 4*I*e) + (2*I*c^5 + 6*c^4*d - 4*I*c^3*d^2 + 4*c^2*d^3 - 6*I*c*d^4 - 2*d^5)*f*e^(2*I*f*x + 2*I*e) + (I*c^5 + c^4*d + 2*I*c^3*d^2 + 2*c^2*d^3 + I*c*d^4 + d^5)*f)","B",0
1097,1,273,0,0.490213," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{4 i \, a c d - 2 \, a d^{2} - 4 \, {\left(-i \, a c d - a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a c^{2} + 2 i \, a c d - a d^{2} + {\left(a c^{2} - 2 i \, a c d - a d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(a c^{2} + a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, c^{5} + 6 \, c^{4} d - 4 i \, c^{3} d^{2} + 4 \, c^{2} d^{3} - 6 i \, c d^{4} - 2 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{5} + c^{4} d + 2 i \, c^{3} d^{2} + 2 \, c^{2} d^{3} + i \, c d^{4} + d^{5}\right)} f}"," ",0,"(4*I*a*c*d - 2*a*d^2 - 4*(-I*a*c*d - a*d^2)*e^(2*I*f*x + 2*I*e) + (a*c^2 + 2*I*a*c*d - a*d^2 + (a*c^2 - 2*I*a*c*d - a*d^2)*e^(4*I*f*x + 4*I*e) + 2*(a*c^2 + a*d^2)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f*e^(4*I*f*x + 4*I*e) + (2*I*c^5 + 6*c^4*d - 4*I*c^3*d^2 + 4*c^2*d^3 - 6*I*c*d^4 - 2*d^5)*f*e^(2*I*f*x + 2*I*e) + (I*c^5 + c^4*d + 2*I*c^3*d^2 + 2*c^2*d^3 + I*c*d^4 + d^5)*f)","B",0
1098,1,715,0,0.517196," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6} - {\left(2 i \, c^{6} - 4 \, c^{5} d + 50 i \, c^{4} d^{2} + 120 \, c^{3} d^{3} - 130 i \, c^{2} d^{4} - 68 \, c d^{5} + 14 i \, d^{6}\right)} f x e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(c^{6} - 4 i \, c^{5} d - 5 \, c^{4} d^{2} + 32 i \, c^{3} d^{3} - 5 \, c^{2} d^{4} + 36 i \, c d^{5} + d^{6} - {\left(4 i \, c^{6} - 16 \, c^{5} d + 76 i \, c^{4} d^{2} + 64 \, c^{3} d^{3} + 44 i \, c^{2} d^{4} + 80 \, c d^{5} - 28 i \, d^{6}\right)} f x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 \, c^{6} - 4 i \, c^{5} d + 2 \, c^{4} d^{2} + 24 i \, c^{3} d^{3} - 58 \, c^{2} d^{4} - 20 i \, c d^{5} - 10 \, d^{6} - {\left(2 i \, c^{6} - 12 \, c^{5} d + 18 i \, c^{4} d^{2} - 24 \, c^{3} d^{3} + 30 i \, c^{2} d^{4} - 12 \, c d^{5} + 14 i \, d^{6}\right)} f x\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left({\left(24 \, c^{4} d^{2} - 64 i \, c^{3} d^{3} - 64 \, c^{2} d^{4} + 32 i \, c d^{5} + 8 \, d^{6}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(48 \, c^{4} d^{2} - 32 i \, c^{3} d^{3} + 32 \, c^{2} d^{4} - 32 i \, c d^{5} - 16 \, d^{6}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 \, c^{4} d^{2} + 32 i \, c^{3} d^{3} + 8 \, d^{6}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(4 i \, a c^{9} + 4 \, a c^{8} d + 16 i \, a c^{7} d^{2} + 16 \, a c^{6} d^{3} + 24 i \, a c^{5} d^{4} + 24 \, a c^{4} d^{5} + 16 i \, a c^{3} d^{6} + 16 \, a c^{2} d^{7} + 4 i \, a c d^{8} + 4 \, a d^{9}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(8 i \, a c^{9} - 8 \, a c^{8} d + 32 i \, a c^{7} d^{2} - 32 \, a c^{6} d^{3} + 48 i \, a c^{5} d^{4} - 48 \, a c^{4} d^{5} + 32 i \, a c^{3} d^{6} - 32 \, a c^{2} d^{7} + 8 i \, a c d^{8} - 8 \, a d^{9}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 i \, a c^{9} - 12 \, a c^{8} d - 32 \, a c^{6} d^{3} - 24 i \, a c^{5} d^{4} - 24 \, a c^{4} d^{5} - 32 i \, a c^{3} d^{6} - 12 i \, a c d^{8} + 4 \, a d^{9}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"-(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6 - (2*I*c^6 - 4*c^5*d + 50*I*c^4*d^2 + 120*c^3*d^3 - 130*I*c^2*d^4 - 68*c*d^5 + 14*I*d^6)*f*x*e^(6*I*f*x + 6*I*e) + (c^6 - 4*I*c^5*d - 5*c^4*d^2 + 32*I*c^3*d^3 - 5*c^2*d^4 + 36*I*c*d^5 + d^6 - (4*I*c^6 - 16*c^5*d + 76*I*c^4*d^2 + 64*c^3*d^3 + 44*I*c^2*d^4 + 80*c*d^5 - 28*I*d^6)*f*x)*e^(4*I*f*x + 4*I*e) + (2*c^6 - 4*I*c^5*d + 2*c^4*d^2 + 24*I*c^3*d^3 - 58*c^2*d^4 - 20*I*c*d^5 - 10*d^6 - (2*I*c^6 - 12*c^5*d + 18*I*c^4*d^2 - 24*c^3*d^3 + 30*I*c^2*d^4 - 12*c*d^5 + 14*I*d^6)*f*x)*e^(2*I*f*x + 2*I*e) + ((24*c^4*d^2 - 64*I*c^3*d^3 - 64*c^2*d^4 + 32*I*c*d^5 + 8*d^6)*e^(6*I*f*x + 6*I*e) + (48*c^4*d^2 - 32*I*c^3*d^3 + 32*c^2*d^4 - 32*I*c*d^5 - 16*d^6)*e^(4*I*f*x + 4*I*e) + (24*c^4*d^2 + 32*I*c^3*d^3 + 8*d^6)*e^(2*I*f*x + 2*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((4*I*a*c^9 + 4*a*c^8*d + 16*I*a*c^7*d^2 + 16*a*c^6*d^3 + 24*I*a*c^5*d^4 + 24*a*c^4*d^5 + 16*I*a*c^3*d^6 + 16*a*c^2*d^7 + 4*I*a*c*d^8 + 4*a*d^9)*f*e^(6*I*f*x + 6*I*e) + (8*I*a*c^9 - 8*a*c^8*d + 32*I*a*c^7*d^2 - 32*a*c^6*d^3 + 48*I*a*c^5*d^4 - 48*a*c^4*d^5 + 32*I*a*c^3*d^6 - 32*a*c^2*d^7 + 8*I*a*c*d^8 - 8*a*d^9)*f*e^(4*I*f*x + 4*I*e) + (4*I*a*c^9 - 12*a*c^8*d - 32*a*c^6*d^3 - 24*I*a*c^5*d^4 - 24*a*c^4*d^5 - 32*I*a*c^3*d^6 - 12*I*a*c*d^8 + 4*a*d^9)*f*e^(2*I*f*x + 2*I*e))","B",0
1099,1,909,0,0.541735," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{i \, c^{7} - c^{6} d + 3 i \, c^{5} d^{2} - 3 \, c^{4} d^{3} + 3 i \, c^{3} d^{4} - 3 \, c^{2} d^{5} + i \, c d^{6} - d^{7} + {\left(4 \, c^{7} + 12 i \, c^{6} d - 4 \, c^{5} d^{2} + 340 i \, c^{4} d^{3} + 940 \, c^{3} d^{4} - 1084 i \, c^{2} d^{5} - 588 \, c d^{6} + 124 i \, d^{7}\right)} f x e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(4 i \, c^{7} + 44 i \, c^{5} d^{2} + 80 \, c^{4} d^{3} - 180 i \, c^{3} d^{4} + 32 \, c^{2} d^{5} - 220 i \, c d^{6} - 48 \, d^{7} + {\left(8 \, c^{7} + 40 i \, c^{6} d - 72 \, c^{5} d^{2} + 600 i \, c^{4} d^{3} + 600 \, c^{3} d^{4} + 312 i \, c^{2} d^{5} + 680 \, c d^{6} - 248 i \, d^{7}\right)} f x\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(9 i \, c^{7} - 13 \, c^{6} d + 71 i \, c^{5} d^{2} + 5 \, c^{4} d^{3} - 45 i \, c^{3} d^{4} + 305 \, c^{2} d^{5} + 85 i \, c d^{6} + 95 \, d^{7} + {\left(4 \, c^{7} + 28 i \, c^{6} d - 84 \, c^{5} d^{2} + 180 i \, c^{4} d^{3} - 180 \, c^{3} d^{4} + 276 i \, c^{2} d^{5} - 92 \, c d^{6} + 124 i \, d^{7}\right)} f x\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 i \, c^{7} - 14 \, c^{6} d + 18 i \, c^{5} d^{2} - 42 \, c^{4} d^{3} + 18 i \, c^{3} d^{4} - 42 \, c^{2} d^{5} + 6 i \, c d^{6} - 14 \, d^{7}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left({\left(160 \, c^{4} d^{3} - 480 i \, c^{3} d^{4} - 544 \, c^{2} d^{5} + 288 i \, c d^{6} + 64 \, d^{7}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(320 \, c^{4} d^{3} - 320 i \, c^{3} d^{4} + 192 \, c^{2} d^{5} - 320 i \, c d^{6} - 128 \, d^{7}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(160 \, c^{4} d^{3} + 160 i \, c^{3} d^{4} + 96 \, c^{2} d^{5} + 32 i \, c d^{6} + 64 \, d^{7}\right)} e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{16 \, {\left(a^{2} c^{10} + 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} + 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} + a^{2} d^{10}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(32 \, a^{2} c^{10} + 64 i \, a^{2} c^{9} d + 96 \, a^{2} c^{8} d^{2} + 256 i \, a^{2} c^{7} d^{3} + 64 \, a^{2} c^{6} d^{4} + 384 i \, a^{2} c^{5} d^{5} - 64 \, a^{2} c^{4} d^{6} + 256 i \, a^{2} c^{3} d^{7} - 96 \, a^{2} c^{2} d^{8} + 64 i \, a^{2} c d^{9} - 32 \, a^{2} d^{10}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(16 \, a^{2} c^{10} + 64 i \, a^{2} c^{9} d - 48 \, a^{2} c^{8} d^{2} + 128 i \, a^{2} c^{7} d^{3} - 224 \, a^{2} c^{6} d^{4} - 224 \, a^{2} c^{4} d^{6} - 128 i \, a^{2} c^{3} d^{7} - 48 \, a^{2} c^{2} d^{8} - 64 i \, a^{2} c d^{9} + 16 \, a^{2} d^{10}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}}"," ",0,"(I*c^7 - c^6*d + 3*I*c^5*d^2 - 3*c^4*d^3 + 3*I*c^3*d^4 - 3*c^2*d^5 + I*c*d^6 - d^7 + (4*c^7 + 12*I*c^6*d - 4*c^5*d^2 + 340*I*c^4*d^3 + 940*c^3*d^4 - 1084*I*c^2*d^5 - 588*c*d^6 + 124*I*d^7)*f*x*e^(8*I*f*x + 8*I*e) + (4*I*c^7 + 44*I*c^5*d^2 + 80*c^4*d^3 - 180*I*c^3*d^4 + 32*c^2*d^5 - 220*I*c*d^6 - 48*d^7 + (8*c^7 + 40*I*c^6*d - 72*c^5*d^2 + 600*I*c^4*d^3 + 600*c^3*d^4 + 312*I*c^2*d^5 + 680*c*d^6 - 248*I*d^7)*f*x)*e^(6*I*f*x + 6*I*e) + (9*I*c^7 - 13*c^6*d + 71*I*c^5*d^2 + 5*c^4*d^3 - 45*I*c^3*d^4 + 305*c^2*d^5 + 85*I*c*d^6 + 95*d^7 + (4*c^7 + 28*I*c^6*d - 84*c^5*d^2 + 180*I*c^4*d^3 - 180*c^3*d^4 + 276*I*c^2*d^5 - 92*c*d^6 + 124*I*d^7)*f*x)*e^(4*I*f*x + 4*I*e) + (6*I*c^7 - 14*c^6*d + 18*I*c^5*d^2 - 42*c^4*d^3 + 18*I*c^3*d^4 - 42*c^2*d^5 + 6*I*c*d^6 - 14*d^7)*e^(2*I*f*x + 2*I*e) - ((160*c^4*d^3 - 480*I*c^3*d^4 - 544*c^2*d^5 + 288*I*c*d^6 + 64*d^7)*e^(8*I*f*x + 8*I*e) + (320*c^4*d^3 - 320*I*c^3*d^4 + 192*c^2*d^5 - 320*I*c*d^6 - 128*d^7)*e^(6*I*f*x + 6*I*e) + (160*c^4*d^3 + 160*I*c^3*d^4 + 96*c^2*d^5 + 32*I*c*d^6 + 64*d^7)*e^(4*I*f*x + 4*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/(16*(a^2*c^10 + 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 + 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 + a^2*d^10)*f*e^(8*I*f*x + 8*I*e) + (32*a^2*c^10 + 64*I*a^2*c^9*d + 96*a^2*c^8*d^2 + 256*I*a^2*c^7*d^3 + 64*a^2*c^6*d^4 + 384*I*a^2*c^5*d^5 - 64*a^2*c^4*d^6 + 256*I*a^2*c^3*d^7 - 96*a^2*c^2*d^8 + 64*I*a^2*c*d^9 - 32*a^2*d^10)*f*e^(6*I*f*x + 6*I*e) + (16*a^2*c^10 + 64*I*a^2*c^9*d - 48*a^2*c^8*d^2 + 128*I*a^2*c^7*d^3 - 224*a^2*c^6*d^4 - 224*a^2*c^4*d^6 - 128*I*a^2*c^3*d^7 - 48*a^2*c^2*d^8 - 64*I*a^2*c*d^9 + 16*a^2*d^10)*f*e^(4*I*f*x + 4*I*e))","B",0
1100,1,1132,0,0.530423," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, c^{8} + 4 i \, c^{7} d + 4 \, c^{6} d^{2} + 12 i \, c^{5} d^{3} + 12 i \, c^{3} d^{5} - 4 \, c^{2} d^{6} + 4 i \, c d^{7} - 2 \, d^{8} + {\left(-12 i \, c^{8} + 48 \, c^{7} d + 48 i \, c^{6} d^{2} + 48 \, c^{5} d^{3} + 3000 i \, c^{4} d^{4} + 9168 \, c^{3} d^{5} - 11088 i \, c^{2} d^{6} - 6192 \, c d^{7} + 1332 i \, d^{8}\right)} f x e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(18 \, c^{8} + 36 i \, c^{7} d + 108 \, c^{6} d^{2} + 396 i \, c^{5} d^{3} + 1080 \, c^{4} d^{4} - 1620 i \, c^{3} d^{5} + 372 \, c^{2} d^{6} - 1980 i \, c d^{7} - 618 \, d^{8} + {\left(-24 i \, c^{8} + 144 \, c^{7} d + 336 i \, c^{6} d^{2} - 336 \, c^{5} d^{3} + 5760 i \, c^{4} d^{4} + 6576 \, c^{3} d^{5} + 2736 i \, c^{2} d^{6} + 7056 \, c d^{7} - 2664 i \, d^{8}\right)} f x\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(45 \, c^{8} + 144 i \, c^{7} d + 72 \, c^{6} d^{2} + 936 i \, c^{5} d^{3} + 450 \, c^{4} d^{4} + 288 i \, c^{3} d^{5} + 2592 \, c^{2} d^{6} + 648 i \, c d^{7} + 1017 \, d^{8} + {\left(-12 i \, c^{8} + 96 \, c^{7} d + 336 i \, c^{6} d^{2} - 672 \, c^{5} d^{3} + 2040 i \, c^{4} d^{4} - 1632 \, c^{3} d^{5} + 3024 i \, c^{2} d^{6} - 864 \, c d^{7} + 1332 i \, d^{8}\right)} f x\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(38 \, c^{8} + 140 i \, c^{7} d - 68 \, c^{6} d^{2} + 420 i \, c^{5} d^{3} - 432 \, c^{4} d^{4} + 420 i \, c^{3} d^{5} - 508 \, c^{2} d^{6} + 140 i \, c d^{7} - 182 \, d^{8}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(13 \, c^{8} + 36 i \, c^{7} d + 16 \, c^{6} d^{2} + 108 i \, c^{5} d^{3} - 30 \, c^{4} d^{4} + 108 i \, c^{3} d^{5} - 56 \, c^{2} d^{6} + 36 i \, c d^{7} - 23 \, d^{8}\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left({\left(1440 \, c^{4} d^{4} - 4608 i \, c^{3} d^{5} - 5568 \, c^{2} d^{6} + 3072 i \, c d^{7} + 672 \, d^{8}\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(2880 \, c^{4} d^{4} - 3456 i \, c^{3} d^{5} + 1536 \, c^{2} d^{6} - 3456 i \, c d^{7} - 1344 \, d^{8}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(1440 \, c^{4} d^{4} + 1152 i \, c^{3} d^{5} + 1344 \, c^{2} d^{6} + 384 i \, c d^{7} + 672 \, d^{8}\right)} e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \log\left(\frac{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}{i \, c + d}\right)}{{\left(-96 i \, a^{3} c^{11} + 96 \, a^{3} c^{10} d - 480 i \, a^{3} c^{9} d^{2} + 480 \, a^{3} c^{8} d^{3} - 960 i \, a^{3} c^{7} d^{4} + 960 \, a^{3} c^{6} d^{5} - 960 i \, a^{3} c^{5} d^{6} + 960 \, a^{3} c^{4} d^{7} - 480 i \, a^{3} c^{3} d^{8} + 480 \, a^{3} c^{2} d^{9} - 96 i \, a^{3} c d^{10} + 96 \, a^{3} d^{11}\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-192 i \, a^{3} c^{11} + 576 \, a^{3} c^{10} d - 192 i \, a^{3} c^{9} d^{2} + 2112 \, a^{3} c^{8} d^{3} + 1152 i \, a^{3} c^{7} d^{4} + 2688 \, a^{3} c^{6} d^{5} + 2688 i \, a^{3} c^{5} d^{6} + 1152 \, a^{3} c^{4} d^{7} + 2112 i \, a^{3} c^{3} d^{8} - 192 \, a^{3} c^{2} d^{9} + 576 i \, a^{3} c d^{10} - 192 \, a^{3} d^{11}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-96 i \, a^{3} c^{11} + 480 \, a^{3} c^{10} d + 672 i \, a^{3} c^{9} d^{2} + 480 \, a^{3} c^{8} d^{3} + 2112 i \, a^{3} c^{7} d^{4} - 1344 \, a^{3} c^{6} d^{5} + 1344 i \, a^{3} c^{5} d^{6} - 2112 \, a^{3} c^{4} d^{7} - 480 i \, a^{3} c^{3} d^{8} - 672 \, a^{3} c^{2} d^{9} - 480 i \, a^{3} c d^{10} + 96 \, a^{3} d^{11}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}}"," ",0,"(2*c^8 + 4*I*c^7*d + 4*c^6*d^2 + 12*I*c^5*d^3 + 12*I*c^3*d^5 - 4*c^2*d^6 + 4*I*c*d^7 - 2*d^8 + (-12*I*c^8 + 48*c^7*d + 48*I*c^6*d^2 + 48*c^5*d^3 + 3000*I*c^4*d^4 + 9168*c^3*d^5 - 11088*I*c^2*d^6 - 6192*c*d^7 + 1332*I*d^8)*f*x*e^(10*I*f*x + 10*I*e) + (18*c^8 + 36*I*c^7*d + 108*c^6*d^2 + 396*I*c^5*d^3 + 1080*c^4*d^4 - 1620*I*c^3*d^5 + 372*c^2*d^6 - 1980*I*c*d^7 - 618*d^8 + (-24*I*c^8 + 144*c^7*d + 336*I*c^6*d^2 - 336*c^5*d^3 + 5760*I*c^4*d^4 + 6576*c^3*d^5 + 2736*I*c^2*d^6 + 7056*c*d^7 - 2664*I*d^8)*f*x)*e^(8*I*f*x + 8*I*e) + (45*c^8 + 144*I*c^7*d + 72*c^6*d^2 + 936*I*c^5*d^3 + 450*c^4*d^4 + 288*I*c^3*d^5 + 2592*c^2*d^6 + 648*I*c*d^7 + 1017*d^8 + (-12*I*c^8 + 96*c^7*d + 336*I*c^6*d^2 - 672*c^5*d^3 + 2040*I*c^4*d^4 - 1632*c^3*d^5 + 3024*I*c^2*d^6 - 864*c*d^7 + 1332*I*d^8)*f*x)*e^(6*I*f*x + 6*I*e) + (38*c^8 + 140*I*c^7*d - 68*c^6*d^2 + 420*I*c^5*d^3 - 432*c^4*d^4 + 420*I*c^3*d^5 - 508*c^2*d^6 + 140*I*c*d^7 - 182*d^8)*e^(4*I*f*x + 4*I*e) + (13*c^8 + 36*I*c^7*d + 16*c^6*d^2 + 108*I*c^5*d^3 - 30*c^4*d^4 + 108*I*c^3*d^5 - 56*c^2*d^6 + 36*I*c*d^7 - 23*d^8)*e^(2*I*f*x + 2*I*e) - ((1440*c^4*d^4 - 4608*I*c^3*d^5 - 5568*c^2*d^6 + 3072*I*c*d^7 + 672*d^8)*e^(10*I*f*x + 10*I*e) + (2880*c^4*d^4 - 3456*I*c^3*d^5 + 1536*c^2*d^6 - 3456*I*c*d^7 - 1344*d^8)*e^(8*I*f*x + 8*I*e) + (1440*c^4*d^4 + 1152*I*c^3*d^5 + 1344*c^2*d^6 + 384*I*c*d^7 + 672*d^8)*e^(6*I*f*x + 6*I*e))*log(((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)/(I*c + d)))/((-96*I*a^3*c^11 + 96*a^3*c^10*d - 480*I*a^3*c^9*d^2 + 480*a^3*c^8*d^3 - 960*I*a^3*c^7*d^4 + 960*a^3*c^6*d^5 - 960*I*a^3*c^5*d^6 + 960*a^3*c^4*d^7 - 480*I*a^3*c^3*d^8 + 480*a^3*c^2*d^9 - 96*I*a^3*c*d^10 + 96*a^3*d^11)*f*e^(10*I*f*x + 10*I*e) + (-192*I*a^3*c^11 + 576*a^3*c^10*d - 192*I*a^3*c^9*d^2 + 2112*a^3*c^8*d^3 + 1152*I*a^3*c^7*d^4 + 2688*a^3*c^6*d^5 + 2688*I*a^3*c^5*d^6 + 1152*a^3*c^4*d^7 + 2112*I*a^3*c^3*d^8 - 192*a^3*c^2*d^9 + 576*I*a^3*c*d^10 - 192*a^3*d^11)*f*e^(8*I*f*x + 8*I*e) + (-96*I*a^3*c^11 + 480*a^3*c^10*d + 672*I*a^3*c^9*d^2 + 480*a^3*c^8*d^3 + 2112*I*a^3*c^7*d^4 - 1344*a^3*c^6*d^5 + 1344*I*a^3*c^5*d^6 - 2112*a^3*c^4*d^7 - 480*I*a^3*c^3*d^8 - 672*a^3*c^2*d^9 - 480*I*a^3*c*d^10 + 96*a^3*d^11)*f*e^(6*I*f*x + 6*I*e))","B",0
1101,1,519,0,0.672853," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 \, a^{6} c - 64 i \, a^{6} d}{f^{2}}} \log\left(\frac{{\left(8 \, a^{3} c + {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 \, a^{6} c - 64 i \, a^{6} d}{f^{2}}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 15 \, {\left(d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 \, a^{6} c - 64 i \, a^{6} d}{f^{2}}} \log\left(\frac{{\left(8 \, a^{3} c + {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 \, a^{6} c - 64 i \, a^{6} d}{f^{2}}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) + {\left(16 i \, a^{3} c^{2} - 112 \, a^{3} c d + 384 i \, a^{3} d^{2} + {\left(16 i \, a^{3} c^{2} - 128 \, a^{3} c d + 624 i \, a^{3} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(32 i \, a^{3} c^{2} - 240 \, a^{3} c d + 912 i \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)}}"," ",0,"1/60*(15*(d^2*f*e^(4*I*f*x + 4*I*e) + 2*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-(64*a^6*c - 64*I*a^6*d)/f^2)*log(1/4*(8*a^3*c + (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(64*a^6*c - 64*I*a^6*d)/f^2) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) - 15*(d^2*f*e^(4*I*f*x + 4*I*e) + 2*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-(64*a^6*c - 64*I*a^6*d)/f^2)*log(1/4*(8*a^3*c + (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(64*a^6*c - 64*I*a^6*d)/f^2) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) + (16*I*a^3*c^2 - 112*a^3*c*d + 384*I*a^3*d^2 + (16*I*a^3*c^2 - 128*a^3*c*d + 624*I*a^3*d^2)*e^(4*I*f*x + 4*I*e) + (32*I*a^3*c^2 - 240*a^3*c*d + 912*I*a^3*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(4*I*f*x + 4*I*e) + 2*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)","B",0
1102,1,407,0,0.484828," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 \, a^{4} c - 16 i \, a^{4} d}{f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c + {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 \, a^{4} c - 16 i \, a^{4} d}{f^{2}}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 3 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 \, a^{4} c - 16 i \, a^{4} d}{f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c + {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 \, a^{4} c - 16 i \, a^{4} d}{f^{2}}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - {\left(8 \, a^{2} c - 40 i \, a^{2} d + {\left(8 \, a^{2} c - 56 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"1/12*(3*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(16*a^4*c - 16*I*a^4*d)/f^2)*log(1/2*(4*a^2*c + (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(16*a^4*c - 16*I*a^4*d)/f^2) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) - 3*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(16*a^4*c - 16*I*a^4*d)/f^2)*log(1/2*(4*a^2*c + (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(16*a^4*c - 16*I*a^4*d)/f^2) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) - (8*a^2*c - 40*I*a^2*d + (8*a^2*c - 56*I*a^2*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
1103,1,312,0,0.469159," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{f \sqrt{-\frac{4 \, a^{2} c - 4 i \, a^{2} d}{f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, a^{2} c - 4 i \, a^{2} d}{f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - f \sqrt{-\frac{4 \, a^{2} c - 4 i \, a^{2} d}{f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, a^{2} c - 4 i \, a^{2} d}{f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) + 8 i \, a \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, f}"," ",0,"1/4*(f*sqrt(-(4*a^2*c - 4*I*a^2*d)/f^2)*log((2*a*c + (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*a^2*c - 4*I*a^2*d)/f^2) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) - f*sqrt(-(4*a^2*c - 4*I*a^2*d)/f^2)*log((2*a*c + (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*a^2*c - 4*I*a^2*d)/f^2) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) + 8*I*a*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/f","B",0
1104,1,686,0,0.558813," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a f \sqrt{-\frac{c - i \, d}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{1}{2} \, {\left({\left(4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c - i \, d}{a^{2} f^{2}}} + 4 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - a f \sqrt{-\frac{c - i \, d}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{1}{2} \, {\left({\left(-4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c - i \, d}{a^{2} f^{2}}} + 4 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 2 \, a f \sqrt{-\frac{i \, c^{2}}{4 \, {\left(i \, a^{2} c - a^{2} d\right)} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} + i \, c d - 2 \, {\left({\left(i \, a c - a d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a c - a d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, c^{2}}{4 \, {\left(i \, a^{2} c - a^{2} d\right)} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(i \, a c - a d\right)} f}\right) - 2 \, a f \sqrt{-\frac{i \, c^{2}}{4 \, {\left(i \, a^{2} c - a^{2} d\right)} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + c^{2} + i \, c d - 2 \, {\left({\left(-i \, a c + a d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a c + a d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i \, c^{2}}{4 \, {\left(i \, a^{2} c - a^{2} d\right)} f^{2}}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(i \, a c - a d\right)} f}\right) + 2 \, \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a f}"," ",0,"1/8*(a*f*sqrt(-(c - I*d)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*((4*I*a*f*e^(2*I*f*x + 2*I*e) + 4*I*a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c - I*d)/(a^2*f^2)) + 4*(c - I*d)*e^(2*I*f*x + 2*I*e) + 4*c)*e^(-2*I*f*x - 2*I*e)) - a*f*sqrt(-(c - I*d)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*((-4*I*a*f*e^(2*I*f*x + 2*I*e) - 4*I*a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c - I*d)/(a^2*f^2)) + 4*(c - I*d)*e^(2*I*f*x + 2*I*e) + 4*c)*e^(-2*I*f*x - 2*I*e)) + 2*a*f*sqrt(-1/4*I*c^2/((I*a^2*c - a^2*d)*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/2*(c^2*e^(2*I*f*x + 2*I*e) + c^2 + I*c*d - 2*((I*a*c - a*d)*f*e^(2*I*f*x + 2*I*e) + (I*a*c - a*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I*c^2/((I*a^2*c - a^2*d)*f^2)))*e^(-2*I*f*x - 2*I*e)/((I*a*c - a*d)*f)) - 2*a*f*sqrt(-1/4*I*c^2/((I*a^2*c - a^2*d)*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/2*(c^2*e^(2*I*f*x + 2*I*e) + c^2 + I*c*d - 2*((-I*a*c + a*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a*c + a*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-1/4*I*c^2/((I*a^2*c - a^2*d)*f^2)))*e^(-2*I*f*x - 2*I*e)/((I*a*c - a*d)*f)) + 2*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(I*e^(2*I*f*x + 2*I*e) + I))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
1105,1,1083,0,0.647367," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left(i \, a^{2} c - a^{2} d\right)} f \sqrt{-\frac{c - i \, d}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{1}{4} \, {\left({\left(8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c - i \, d}{a^{4} f^{2}}} + 8 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left(-i \, a^{2} c + a^{2} d\right)} f \sqrt{-\frac{c - i \, d}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{1}{4} \, {\left({\left(-8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c - i \, d}{a^{4} f^{2}}} + 8 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 4 \, {\left(-i \, a^{2} c + a^{2} d\right)} f \sqrt{\frac{-4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} - i \, d^{4}}{{\left(64 i \, a^{4} c^{3} - 192 \, a^{4} c^{2} d - 192 i \, a^{4} c d^{2} + 64 \, a^{4} d^{3}\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(-2 i \, c^{3} + 4 \, c^{2} d + i \, c d^{2} + d^{3} + 8 \, {\left({\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} - i \, d^{4}}{{\left(64 i \, a^{4} c^{3} - 192 \, a^{4} c^{2} d - 192 i \, a^{4} c d^{2} + 64 \, a^{4} d^{3}\right)} f^{2}}} + {\left(-2 i \, c^{3} + 2 \, c^{2} d - i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f}\right) + 4 \, {\left(i \, a^{2} c - a^{2} d\right)} f \sqrt{\frac{-4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} - i \, d^{4}}{{\left(64 i \, a^{4} c^{3} - 192 \, a^{4} c^{2} d - 192 i \, a^{4} c d^{2} + 64 \, a^{4} d^{3}\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(-2 i \, c^{3} + 4 \, c^{2} d + i \, c d^{2} + d^{3} - 8 \, {\left({\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} - i \, d^{4}}{{\left(64 i \, a^{4} c^{3} - 192 \, a^{4} c^{2} d - 192 i \, a^{4} c d^{2} + 64 \, a^{4} d^{3}\right)} f^{2}}} + {\left(-2 i \, c^{3} + 2 \, c^{2} d - i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f}\right) - {\left({\left(3 \, c + 2 i \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 \, c + 3 i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, {\left(i \, a^{2} c - a^{2} d\right)} f}"," ",0,"1/16*((I*a^2*c - a^2*d)*f*sqrt(-(c - I*d)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*((8*I*a^2*f*e^(2*I*f*x + 2*I*e) + 8*I*a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c - I*d)/(a^4*f^2)) + 8*(c - I*d)*e^(2*I*f*x + 2*I*e) + 8*c)*e^(-2*I*f*x - 2*I*e)) + (-I*a^2*c + a^2*d)*f*sqrt(-(c - I*d)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*((-8*I*a^2*f*e^(2*I*f*x + 2*I*e) - 8*I*a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c - I*d)/(a^4*f^2)) + 8*(c - I*d)*e^(2*I*f*x + 2*I*e) + 8*c)*e^(-2*I*f*x - 2*I*e)) + 4*(-I*a^2*c + a^2*d)*f*sqrt((-4*I*c^4 + 8*c^3*d + 4*c*d^3 - I*d^4)/((64*I*a^4*c^3 - 192*a^4*c^2*d - 192*I*a^4*c*d^2 + 64*a^4*d^3)*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(-2*I*c^3 + 4*c^2*d + I*c*d^2 + d^3 + 8*((a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*e^(2*I*f*x + 2*I*e) + (a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^4 + 8*c^3*d + 4*c*d^3 - I*d^4)/((64*I*a^4*c^3 - 192*a^4*c^2*d - 192*I*a^4*c*d^2 + 64*a^4*d^3)*f^2)) + (-2*I*c^3 + 2*c^2*d - I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f)) + 4*(I*a^2*c - a^2*d)*f*sqrt((-4*I*c^4 + 8*c^3*d + 4*c*d^3 - I*d^4)/((64*I*a^4*c^3 - 192*a^4*c^2*d - 192*I*a^4*c*d^2 + 64*a^4*d^3)*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(-2*I*c^3 + 4*c^2*d + I*c*d^2 + d^3 - 8*((a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*e^(2*I*f*x + 2*I*e) + (a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^4 + 8*c^3*d + 4*c*d^3 - I*d^4)/((64*I*a^4*c^3 - 192*a^4*c^2*d - 192*I*a^4*c*d^2 + 64*a^4*d^3)*f^2)) + (-2*I*c^3 + 2*c^2*d - I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f)) - ((3*c + 2*I*d)*e^(4*I*f*x + 4*I*e) + (4*c + 3*I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/((I*a^2*c - a^2*d)*f)","B",0
1106,1,1448,0,1.051233," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f \sqrt{-\frac{c - i \, d}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{1}{8} \, {\left({\left(16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c - i \, d}{a^{6} f^{2}}} + 16 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 3 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f \sqrt{-\frac{c - i \, d}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{1}{8} \, {\left({\left(-16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, a^{3} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c - i \, d}{a^{6} f^{2}}} + 16 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 24 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f \sqrt{\frac{4 i \, c^{6} - 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} + 4 \, c d^{5} - 4 i \, d^{6}}{{\left(-256 i \, a^{6} c^{5} + 1280 \, a^{6} c^{4} d + 2560 i \, a^{6} c^{3} d^{2} - 2560 \, a^{6} c^{2} d^{3} - 1280 i \, a^{6} c d^{4} + 256 \, a^{6} d^{5}\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{4} + 6 i \, c^{3} d - 5 \, c^{2} d^{2} + i \, c d^{3} - 2 \, d^{4} - {\left({\left(16 i \, a^{3} c^{3} - 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, a^{3} c^{3} - 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{6} - 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} + 4 \, c d^{5} - 4 i \, d^{6}}{{\left(-256 i \, a^{6} c^{5} + 1280 \, a^{6} c^{4} d + 2560 i \, a^{6} c^{3} d^{2} - 2560 \, a^{6} c^{2} d^{3} - 1280 i \, a^{6} c d^{4} + 256 \, a^{6} d^{5}\right)} f^{2}}} + {\left(2 \, c^{4} + 4 i \, c^{3} d - c^{2} d^{2} + 2 i \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(16 i \, a^{3} c^{3} - 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} f}\right) - 24 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f \sqrt{\frac{4 i \, c^{6} - 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} + 4 \, c d^{5} - 4 i \, d^{6}}{{\left(-256 i \, a^{6} c^{5} + 1280 \, a^{6} c^{4} d + 2560 i \, a^{6} c^{3} d^{2} - 2560 \, a^{6} c^{2} d^{3} - 1280 i \, a^{6} c d^{4} + 256 \, a^{6} d^{5}\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{4} + 6 i \, c^{3} d - 5 \, c^{2} d^{2} + i \, c d^{3} - 2 \, d^{4} - {\left({\left(-16 i \, a^{3} c^{3} + 48 \, a^{3} c^{2} d + 48 i \, a^{3} c d^{2} - 16 \, a^{3} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-16 i \, a^{3} c^{3} + 48 \, a^{3} c^{2} d + 48 i \, a^{3} c d^{2} - 16 \, a^{3} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{6} - 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} + 4 \, c d^{5} - 4 i \, d^{6}}{{\left(-256 i \, a^{6} c^{5} + 1280 \, a^{6} c^{4} d + 2560 i \, a^{6} c^{3} d^{2} - 2560 \, a^{6} c^{2} d^{3} - 1280 i \, a^{6} c d^{4} + 256 \, a^{6} d^{5}\right)} f^{2}}} + {\left(2 \, c^{4} + 4 i \, c^{3} d - c^{2} d^{2} + 2 i \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(16 i \, a^{3} c^{3} - 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} f}\right) - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} + {\left(-11 i \, c^{2} + 18 \, c d + 4 i \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-18 i \, c^{2} + 31 \, c d + 10 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-9 i \, c^{2} + 17 \, c d + 8 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f}"," ",0,"1/96*(3*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*sqrt(-(c - I*d)/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*((16*I*a^3*f*e^(2*I*f*x + 2*I*e) + 16*I*a^3*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c - I*d)/(a^6*f^2)) + 16*(c - I*d)*e^(2*I*f*x + 2*I*e) + 16*c)*e^(-2*I*f*x - 2*I*e)) - 3*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*sqrt(-(c - I*d)/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*((-16*I*a^3*f*e^(2*I*f*x + 2*I*e) - 16*I*a^3*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c - I*d)/(a^6*f^2)) + 16*(c - I*d)*e^(2*I*f*x + 2*I*e) + 16*c)*e^(-2*I*f*x - 2*I*e)) + 24*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*sqrt((4*I*c^6 - 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 + 4*c*d^5 - 4*I*d^6)/((-256*I*a^6*c^5 + 1280*a^6*c^4*d + 2560*I*a^6*c^3*d^2 - 2560*a^6*c^2*d^3 - 1280*I*a^6*c*d^4 + 256*a^6*d^5)*f^2))*e^(6*I*f*x + 6*I*e)*log(-(2*c^4 + 6*I*c^3*d - 5*c^2*d^2 + I*c*d^3 - 2*d^4 - ((16*I*a^3*c^3 - 48*a^3*c^2*d - 48*I*a^3*c*d^2 + 16*a^3*d^3)*f*e^(2*I*f*x + 2*I*e) + (16*I*a^3*c^3 - 48*a^3*c^2*d - 48*I*a^3*c*d^2 + 16*a^3*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^6 - 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 + 4*c*d^5 - 4*I*d^6)/((-256*I*a^6*c^5 + 1280*a^6*c^4*d + 2560*I*a^6*c^3*d^2 - 2560*a^6*c^2*d^3 - 1280*I*a^6*c*d^4 + 256*a^6*d^5)*f^2)) + (2*c^4 + 4*I*c^3*d - c^2*d^2 + 2*I*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((16*I*a^3*c^3 - 48*a^3*c^2*d - 48*I*a^3*c*d^2 + 16*a^3*d^3)*f)) - 24*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*sqrt((4*I*c^6 - 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 + 4*c*d^5 - 4*I*d^6)/((-256*I*a^6*c^5 + 1280*a^6*c^4*d + 2560*I*a^6*c^3*d^2 - 2560*a^6*c^2*d^3 - 1280*I*a^6*c*d^4 + 256*a^6*d^5)*f^2))*e^(6*I*f*x + 6*I*e)*log(-(2*c^4 + 6*I*c^3*d - 5*c^2*d^2 + I*c*d^3 - 2*d^4 - ((-16*I*a^3*c^3 + 48*a^3*c^2*d + 48*I*a^3*c*d^2 - 16*a^3*d^3)*f*e^(2*I*f*x + 2*I*e) + (-16*I*a^3*c^3 + 48*a^3*c^2*d + 48*I*a^3*c*d^2 - 16*a^3*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^6 - 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 + 4*c*d^5 - 4*I*d^6)/((-256*I*a^6*c^5 + 1280*a^6*c^4*d + 2560*I*a^6*c^3*d^2 - 2560*a^6*c^2*d^3 - 1280*I*a^6*c*d^4 + 256*a^6*d^5)*f^2)) + (2*c^4 + 4*I*c^3*d - c^2*d^2 + 2*I*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((16*I*a^3*c^3 - 48*a^3*c^2*d - 48*I*a^3*c*d^2 + 16*a^3*d^3)*f)) - (-2*I*c^2 + 4*c*d + 2*I*d^2 + (-11*I*c^2 + 18*c*d + 4*I*d^2)*e^(6*I*f*x + 6*I*e) + (-18*I*c^2 + 31*c*d + 10*I*d^2)*e^(4*I*f*x + 4*I*e) + (-9*I*c^2 + 17*c*d + 8*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/((a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f)","B",0
1107,1,790,0,0.958969," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{105 \, {\left(d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 \, a^{6} c^{3} - 192 i \, a^{6} c^{2} d - 192 \, a^{6} c d^{2} + 64 i \, a^{6} d^{3}}{f^{2}}} \log\left(-\frac{{\left(8 i \, a^{3} c^{2} + 8 \, a^{3} c d + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 \, a^{6} c^{3} - 192 i \, a^{6} c^{2} d - 192 \, a^{6} c d^{2} + 64 i \, a^{6} d^{3}}{f^{2}}} + {\left(8 i \, a^{3} c^{2} + 16 \, a^{3} c d - 8 i \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(-i \, a^{3} c - a^{3} d\right)}}\right) - 105 \, {\left(d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 \, a^{6} c^{3} - 192 i \, a^{6} c^{2} d - 192 \, a^{6} c d^{2} + 64 i \, a^{6} d^{3}}{f^{2}}} \log\left(-\frac{{\left(8 i \, a^{3} c^{2} + 8 \, a^{3} c d - {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 \, a^{6} c^{3} - 192 i \, a^{6} c^{2} d - 192 \, a^{6} c d^{2} + 64 i \, a^{6} d^{3}}{f^{2}}} + {\left(8 i \, a^{3} c^{2} + 16 \, a^{3} c d - 8 i \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(-i \, a^{3} c - a^{3} d\right)}}\right) - {\left(48 i \, a^{3} c^{3} - 480 \, a^{3} c^{2} d + 3664 i \, a^{3} c d^{2} + 2624 \, a^{3} d^{3} + {\left(48 i \, a^{3} c^{3} - 528 \, a^{3} c^{2} d + 5680 i \, a^{3} c d^{2} + 5104 \, a^{3} d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(144 i \, a^{3} c^{3} - 1536 \, a^{3} c^{2} d + 14256 i \, a^{3} c d^{2} + 10336 \, a^{3} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(144 i \, a^{3} c^{3} - 1488 \, a^{3} c^{2} d + 12240 i \, a^{3} c d^{2} + 8816 \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{420 \, {\left(d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)}}"," ",0,"-1/420*(105*(d^2*f*e^(6*I*f*x + 6*I*e) + 3*d^2*f*e^(4*I*f*x + 4*I*e) + 3*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-(64*a^6*c^3 - 192*I*a^6*c^2*d - 192*a^6*c*d^2 + 64*I*a^6*d^3)/f^2)*log(-1/4*(8*I*a^3*c^2 + 8*a^3*c*d + (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(64*a^6*c^3 - 192*I*a^6*c^2*d - 192*a^6*c*d^2 + 64*I*a^6*d^3)/f^2) + (8*I*a^3*c^2 + 16*a^3*c*d - 8*I*a^3*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(-I*a^3*c - a^3*d)) - 105*(d^2*f*e^(6*I*f*x + 6*I*e) + 3*d^2*f*e^(4*I*f*x + 4*I*e) + 3*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-(64*a^6*c^3 - 192*I*a^6*c^2*d - 192*a^6*c*d^2 + 64*I*a^6*d^3)/f^2)*log(-1/4*(8*I*a^3*c^2 + 8*a^3*c*d - (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(64*a^6*c^3 - 192*I*a^6*c^2*d - 192*a^6*c*d^2 + 64*I*a^6*d^3)/f^2) + (8*I*a^3*c^2 + 16*a^3*c*d - 8*I*a^3*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(-I*a^3*c - a^3*d)) - (48*I*a^3*c^3 - 480*a^3*c^2*d + 3664*I*a^3*c*d^2 + 2624*a^3*d^3 + (48*I*a^3*c^3 - 528*a^3*c^2*d + 5680*I*a^3*c*d^2 + 5104*a^3*d^3)*e^(6*I*f*x + 6*I*e) + (144*I*a^3*c^3 - 1536*a^3*c^2*d + 14256*I*a^3*c*d^2 + 10336*a^3*d^3)*e^(4*I*f*x + 4*I*e) + (144*I*a^3*c^3 - 1488*a^3*c^2*d + 12240*I*a^3*c*d^2 + 8816*a^3*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(6*I*f*x + 6*I*e) + 3*d^2*f*e^(4*I*f*x + 4*I*e) + 3*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)","B",0
1108,1,650,0,0.598360," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 \, a^{4} c^{3} - 48 i \, a^{4} c^{2} d - 48 \, a^{4} c d^{2} + 16 i \, a^{4} d^{3}}{f^{2}}} \log\left(-\frac{{\left(4 i \, a^{2} c^{2} + 4 \, a^{2} c d + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 \, a^{4} c^{3} - 48 i \, a^{4} c^{2} d - 48 \, a^{4} c d^{2} + 16 i \, a^{4} d^{3}}{f^{2}}} + {\left(4 i \, a^{2} c^{2} + 8 \, a^{2} c d - 4 i \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(-i \, a^{2} c - a^{2} d\right)}}\right) - 15 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 \, a^{4} c^{3} - 48 i \, a^{4} c^{2} d - 48 \, a^{4} c d^{2} + 16 i \, a^{4} d^{3}}{f^{2}}} \log\left(-\frac{{\left(4 i \, a^{2} c^{2} + 4 \, a^{2} c d - {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 \, a^{4} c^{3} - 48 i \, a^{4} c^{2} d - 48 \, a^{4} c d^{2} + 16 i \, a^{4} d^{3}}{f^{2}}} + {\left(4 i \, a^{2} c^{2} + 8 \, a^{2} c d - 4 i \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(-i \, a^{2} c - a^{2} d\right)}}\right) + 8 \, {\left(3 \, a^{2} c^{2} - 34 i \, a^{2} c d - 23 \, a^{2} d^{2} + {\left(3 \, a^{2} c^{2} - 46 i \, a^{2} c d - 43 \, a^{2} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(3 \, a^{2} c^{2} - 40 i \, a^{2} c d - 27 \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"-1/60*(15*(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(16*a^4*c^3 - 48*I*a^4*c^2*d - 48*a^4*c*d^2 + 16*I*a^4*d^3)/f^2)*log(-1/2*(4*I*a^2*c^2 + 4*a^2*c*d + (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(16*a^4*c^3 - 48*I*a^4*c^2*d - 48*a^4*c*d^2 + 16*I*a^4*d^3)/f^2) + (4*I*a^2*c^2 + 8*a^2*c*d - 4*I*a^2*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(-I*a^2*c - a^2*d)) - 15*(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(16*a^4*c^3 - 48*I*a^4*c^2*d - 48*a^4*c*d^2 + 16*I*a^4*d^3)/f^2)*log(-1/2*(4*I*a^2*c^2 + 4*a^2*c*d - (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(16*a^4*c^3 - 48*I*a^4*c^2*d - 48*a^4*c*d^2 + 16*I*a^4*d^3)/f^2) + (4*I*a^2*c^2 + 8*a^2*c*d - 4*I*a^2*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(-I*a^2*c - a^2*d)) + 8*(3*a^2*c^2 - 34*I*a^2*c*d - 23*a^2*d^2 + (3*a^2*c^2 - 46*I*a^2*c*d - 43*a^2*d^2)*e^(4*I*f*x + 4*I*e) + 2*(3*a^2*c^2 - 40*I*a^2*c*d - 27*a^2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
1109,1,506,0,0.555218," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{4 \, a^{2} c^{3} - 12 i \, a^{2} c^{2} d - 12 \, a^{2} c d^{2} + 4 i \, a^{2} d^{3}}{f^{2}}} \log\left(\frac{{\left(2 i \, a c^{2} + 2 \, a c d + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, a^{2} c^{3} - 12 i \, a^{2} c^{2} d - 12 \, a^{2} c d^{2} + 4 i \, a^{2} d^{3}}{f^{2}}} + {\left(2 i \, a c^{2} + 4 \, a c d - 2 i \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, a c + a d}\right) - 3 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{4 \, a^{2} c^{3} - 12 i \, a^{2} c^{2} d - 12 \, a^{2} c d^{2} + 4 i \, a^{2} d^{3}}{f^{2}}} \log\left(\frac{{\left(2 i \, a c^{2} + 2 \, a c d - {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, a^{2} c^{3} - 12 i \, a^{2} c^{2} d - 12 \, a^{2} c d^{2} + 4 i \, a^{2} d^{3}}{f^{2}}} + {\left(2 i \, a c^{2} + 4 \, a c d - 2 i \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, a c + a d}\right) + 16 \, {\left(-2 i \, a c - a d + 2 \, {\left(-i \, a c - a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/12*(3*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(4*a^2*c^3 - 12*I*a^2*c^2*d - 12*a^2*c*d^2 + 4*I*a^2*d^3)/f^2)*log((2*I*a*c^2 + 2*a*c*d + (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*a^2*c^3 - 12*I*a^2*c^2*d - 12*a^2*c*d^2 + 4*I*a^2*d^3)/f^2) + (2*I*a*c^2 + 4*a*c*d - 2*I*a*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*a*c + a*d)) - 3*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(4*a^2*c^3 - 12*I*a^2*c^2*d - 12*a^2*c*d^2 + 4*I*a^2*d^3)/f^2)*log((2*I*a*c^2 + 2*a*c*d - (f*e^(2*I*f*x + 2*I*e) + f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*a^2*c^3 - 12*I*a^2*c^2*d - 12*a^2*c*d^2 + 4*I*a^2*d^3)/f^2) + (2*I*a*c^2 + 4*a*c*d - 2*I*a*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*a*c + a*d)) + 16*(-2*I*a*c - a*d + 2*(-I*a*c - a*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
1110,1,779,0,0.532102," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{2} + 2 \, c d + 2 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{2} f^{2}}} + {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, c + d}\right) - a f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{2} + 2 \, c d - 2 \, {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{2} f^{2}}} + {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, c + d}\right) - a f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 4 i \, d^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, c^{2} + c d + 2 i \, d^{2} + {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 4 i \, d^{3}}{a^{2} f^{2}}} + {\left(i \, c^{2} + 2 \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a f}\right) + a f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 4 i \, d^{3}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, c^{2} + c d + 2 i \, d^{2} - {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 4 i \, d^{3}}{a^{2} f^{2}}} + {\left(i \, c^{2} + 2 \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a f}\right) - 2 \, {\left({\left(i \, c - d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a f}"," ",0,"-1/8*(a*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((2*I*c^2 + 2*c*d + 2*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^2*f^2)) + (2*I*c^2 + 4*c*d - 2*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*c + d)) - a*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log((2*I*c^2 + 2*c*d - 2*(a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^2*f^2)) + (2*I*c^2 + 4*c*d - 2*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*c + d)) - a*f*sqrt(-(c^3 - 3*I*c^2*d - 4*I*d^3)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(I*c^2 + c*d + 2*I*d^2 + (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 4*I*d^3)/(a^2*f^2)) + (I*c^2 + 2*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f)) + a*f*sqrt(-(c^3 - 3*I*c^2*d - 4*I*d^3)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(I*c^2 + c*d + 2*I*d^2 - (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 4*I*d^3)/(a^2*f^2)) + (I*c^2 + 2*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f)) - 2*((I*c - d)*e^(2*I*f*x + 2*I*e) + I*c - d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
1111,1,982,0,0.669108," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{2} + 2 \, c d + 2 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{4} f^{2}}} + {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, c + d}\right) - 2 \, a^{2} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{2} + 2 \, c d - 2 \, {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{4} f^{2}}} + {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, c + d}\right) - a^{2} f \sqrt{-\frac{4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} + i \, d^{4}}{{\left(i \, a^{4} c - a^{4} d\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{3} + 3 \, c d^{2} + i \, d^{3} - {\left({\left(i \, a^{2} c - a^{2} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a^{2} c - a^{2} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} + i \, d^{4}}{{\left(i \, a^{4} c - a^{4} d\right)} f^{2}}} + {\left(2 \, c^{3} - 2 i \, c^{2} d + c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, {\left(i \, a^{2} c - a^{2} d\right)} f}\right) + a^{2} f \sqrt{-\frac{4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} + i \, d^{4}}{{\left(i \, a^{4} c - a^{4} d\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{3} + 3 \, c d^{2} + i \, d^{3} - {\left({\left(-i \, a^{2} c + a^{2} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a^{2} c + a^{2} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, c^{4} + 8 \, c^{3} d + 4 \, c d^{3} + i \, d^{4}}{{\left(i \, a^{4} c - a^{4} d\right)} f^{2}}} + {\left(2 \, c^{3} - 2 i \, c^{2} d + c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, {\left(i \, a^{2} c - a^{2} d\right)} f}\right) - 2 \, {\left({\left(3 i \, c + 2 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{32 \, a^{2} f}"," ",0,"-1/32*(2*a^2*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log((2*I*c^2 + 2*c*d + 2*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^4*f^2)) + (2*I*c^2 + 4*c*d - 2*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*c + d)) - 2*a^2*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log((2*I*c^2 + 2*c*d - 2*(a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^4*f^2)) + (2*I*c^2 + 4*c*d - 2*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*c + d)) - a^2*f*sqrt(-(4*I*c^4 + 8*c^3*d + 4*c*d^3 + I*d^4)/((I*a^4*c - a^4*d)*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(2*c^3 + 3*c*d^2 + I*d^3 - ((I*a^2*c - a^2*d)*f*e^(2*I*f*x + 2*I*e) + (I*a^2*c - a^2*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*I*c^4 + 8*c^3*d + 4*c*d^3 + I*d^4)/((I*a^4*c - a^4*d)*f^2)) + (2*c^3 - 2*I*c^2*d + c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((I*a^2*c - a^2*d)*f)) + a^2*f*sqrt(-(4*I*c^4 + 8*c^3*d + 4*c*d^3 + I*d^4)/((I*a^4*c - a^4*d)*f^2))*e^(4*I*f*x + 4*I*e)*log(-1/8*(2*c^3 + 3*c*d^2 + I*d^3 - ((-I*a^2*c + a^2*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a^2*c + a^2*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*I*c^4 + 8*c^3*d + 4*c*d^3 + I*d^4)/((I*a^4*c - a^4*d)*f^2)) + (2*c^3 - 2*I*c^2*d + c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((I*a^2*c - a^2*d)*f)) - 2*((3*I*c + 2*d)*e^(4*I*f*x + 4*I*e) + (4*I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
1112,1,1234,0,0.961737," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(-i \, a^{3} c + a^{3} d\right)} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{2} + 2 \, c d + 2 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{6} f^{2}}} + {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, c + d}\right) + 3 \, {\left(i \, a^{3} c - a^{3} d\right)} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{2} + 2 \, c d - 2 \, {\left(a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{3} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{6} f^{2}}} + {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{i \, c + d}\right) + 24 \, {\left(-i \, a^{3} c + a^{3} d\right)} f \sqrt{\frac{-4 i \, c^{6} - 12 i \, c^{4} d^{2} - 9 i \, c^{2} d^{4}}{{\left(256 i \, a^{6} c^{3} - 768 \, a^{6} c^{2} d - 768 i \, a^{6} c d^{2} + 256 \, a^{6} d^{3}\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(-2 i \, c^{4} + 2 \, c^{3} d - 3 i \, c^{2} d^{2} + 3 \, c d^{3} + 16 \, {\left({\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{6} - 12 i \, c^{4} d^{2} - 9 i \, c^{2} d^{4}}{{\left(256 i \, a^{6} c^{3} - 768 \, a^{6} c^{2} d - 768 i \, a^{6} c d^{2} + 256 \, a^{6} d^{3}\right)} f^{2}}} + {\left(-2 i \, c^{4} - 3 i \, c^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{16 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f}\right) + 24 \, {\left(i \, a^{3} c - a^{3} d\right)} f \sqrt{\frac{-4 i \, c^{6} - 12 i \, c^{4} d^{2} - 9 i \, c^{2} d^{4}}{{\left(256 i \, a^{6} c^{3} - 768 \, a^{6} c^{2} d - 768 i \, a^{6} c d^{2} + 256 \, a^{6} d^{3}\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(-2 i \, c^{4} + 2 \, c^{3} d - 3 i \, c^{2} d^{2} + 3 \, c d^{3} - 16 \, {\left({\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{6} - 12 i \, c^{4} d^{2} - 9 i \, c^{2} d^{4}}{{\left(256 i \, a^{6} c^{3} - 768 \, a^{6} c^{2} d - 768 i \, a^{6} c d^{2} + 256 \, a^{6} d^{3}\right)} f^{2}}} + {\left(-2 i \, c^{4} - 3 i \, c^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{16 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f}\right) - {\left(2 \, c^{2} + 4 i \, c d - 2 \, d^{2} + {\left(11 \, c^{2} + 8 \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(18 \, c^{2} + 7 i \, c d + 8 \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 \, c^{2} + 11 i \, c d - 2 \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{96 \, {\left(i \, a^{3} c - a^{3} d\right)} f}"," ",0,"1/96*(3*(-I*a^3*c + a^3*d)*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((2*I*c^2 + 2*c*d + 2*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^6*f^2)) + (2*I*c^2 + 4*c*d - 2*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*c + d)) + 3*(I*a^3*c - a^3*d)*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log((2*I*c^2 + 2*c*d - 2*(a^3*f*e^(2*I*f*x + 2*I*e) + a^3*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^6*f^2)) + (2*I*c^2 + 4*c*d - 2*I*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(I*c + d)) + 24*(-I*a^3*c + a^3*d)*f*sqrt((-4*I*c^6 - 12*I*c^4*d^2 - 9*I*c^2*d^4)/((256*I*a^6*c^3 - 768*a^6*c^2*d - 768*I*a^6*c*d^2 + 256*a^6*d^3)*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/16*(-2*I*c^4 + 2*c^3*d - 3*I*c^2*d^2 + 3*c*d^3 + 16*((a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*e^(2*I*f*x + 2*I*e) + (a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^6 - 12*I*c^4*d^2 - 9*I*c^2*d^4)/((256*I*a^6*c^3 - 768*a^6*c^2*d - 768*I*a^6*c*d^2 + 256*a^6*d^3)*f^2)) + (-2*I*c^4 - 3*I*c^2*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f)) + 24*(I*a^3*c - a^3*d)*f*sqrt((-4*I*c^6 - 12*I*c^4*d^2 - 9*I*c^2*d^4)/((256*I*a^6*c^3 - 768*a^6*c^2*d - 768*I*a^6*c*d^2 + 256*a^6*d^3)*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/16*(-2*I*c^4 + 2*c^3*d - 3*I*c^2*d^2 + 3*c*d^3 - 16*((a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*e^(2*I*f*x + 2*I*e) + (a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^6 - 12*I*c^4*d^2 - 9*I*c^2*d^4)/((256*I*a^6*c^3 - 768*a^6*c^2*d - 768*I*a^6*c*d^2 + 256*a^6*d^3)*f^2)) + (-2*I*c^4 - 3*I*c^2*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f)) - (2*c^2 + 4*I*c*d - 2*d^2 + (11*c^2 + 8*d^2)*e^(6*I*f*x + 6*I*e) + (18*c^2 + 7*I*c*d + 8*d^2)*e^(4*I*f*x + 4*I*e) + (9*c^2 + 11*I*c*d - 2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/((I*a^3*c - a^3*d)*f)","B",0
1113,1,1094,0,1.153310," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{315 \, {\left(d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 \, a^{6} c^{5} - 320 i \, a^{6} c^{4} d - 640 \, a^{6} c^{3} d^{2} + 640 i \, a^{6} c^{2} d^{3} + 320 \, a^{6} c d^{4} - 64 i \, a^{6} d^{5}}{f^{2}}} \log\left(\frac{{\left(8 \, a^{3} c^{3} - 16 i \, a^{3} c^{2} d - 8 \, a^{3} c d^{2} - {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 \, a^{6} c^{5} - 320 i \, a^{6} c^{4} d - 640 \, a^{6} c^{3} d^{2} + 640 i \, a^{6} c^{2} d^{3} + 320 \, a^{6} c d^{4} - 64 i \, a^{6} d^{5}}{f^{2}}} + {\left(8 \, a^{3} c^{3} - 24 i \, a^{3} c^{2} d - 24 \, a^{3} c d^{2} + 8 i \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(a^{3} c^{2} - 2 i \, a^{3} c d - a^{3} d^{2}\right)}}\right) - 315 \, {\left(d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 \, a^{6} c^{5} - 320 i \, a^{6} c^{4} d - 640 \, a^{6} c^{3} d^{2} + 640 i \, a^{6} c^{2} d^{3} + 320 \, a^{6} c d^{4} - 64 i \, a^{6} d^{5}}{f^{2}}} \log\left(\frac{{\left(8 \, a^{3} c^{3} - 16 i \, a^{3} c^{2} d - 8 \, a^{3} c d^{2} - {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{64 \, a^{6} c^{5} - 320 i \, a^{6} c^{4} d - 640 \, a^{6} c^{3} d^{2} + 640 i \, a^{6} c^{2} d^{3} + 320 \, a^{6} c d^{4} - 64 i \, a^{6} d^{5}}{f^{2}}} + {\left(8 \, a^{3} c^{3} - 24 i \, a^{3} c^{2} d - 24 \, a^{3} c d^{2} + 8 i \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(a^{3} c^{2} - 2 i \, a^{3} c d - a^{3} d^{2}\right)}}\right) - {\left(80 i \, a^{3} c^{4} - 1040 \, a^{3} c^{3} d + 12816 i \, a^{3} c^{2} d^{2} + 18608 \, a^{3} c d^{3} - 7936 i \, a^{3} d^{4} + {\left(80 i \, a^{3} c^{4} - 1120 \, a^{3} c^{3} d + 19296 i \, a^{3} c^{2} d^{2} + 34912 \, a^{3} c d^{3} - 16816 i \, a^{3} d^{4}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(320 i \, a^{3} c^{4} - 4400 \, a^{3} c^{3} d + 68304 i \, a^{3} c^{2} d^{2} + 107344 \, a^{3} c d^{3} - 43760 i \, a^{3} d^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(480 i \, a^{3} c^{4} - 6480 \, a^{3} c^{3} d + 91536 i \, a^{3} c^{2} d^{2} + 134640 \, a^{3} c d^{3} - 58128 i \, a^{3} d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(320 i \, a^{3} c^{4} - 4240 \, a^{3} c^{3} d + 55344 i \, a^{3} c^{2} d^{2} + 80816 \, a^{3} c d^{3} - 34640 i \, a^{3} d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{1260 \, {\left(d^{2} f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)}}"," ",0,"-1/1260*(315*(d^2*f*e^(8*I*f*x + 8*I*e) + 4*d^2*f*e^(6*I*f*x + 6*I*e) + 6*d^2*f*e^(4*I*f*x + 4*I*e) + 4*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-(64*a^6*c^5 - 320*I*a^6*c^4*d - 640*a^6*c^3*d^2 + 640*I*a^6*c^2*d^3 + 320*a^6*c*d^4 - 64*I*a^6*d^5)/f^2)*log(1/4*(8*a^3*c^3 - 16*I*a^3*c^2*d - 8*a^3*c*d^2 - (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(64*a^6*c^5 - 320*I*a^6*c^4*d - 640*a^6*c^3*d^2 + 640*I*a^6*c^2*d^3 + 320*a^6*c*d^4 - 64*I*a^6*d^5)/f^2) + (8*a^3*c^3 - 24*I*a^3*c^2*d - 24*a^3*c*d^2 + 8*I*a^3*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a^3*c^2 - 2*I*a^3*c*d - a^3*d^2)) - 315*(d^2*f*e^(8*I*f*x + 8*I*e) + 4*d^2*f*e^(6*I*f*x + 6*I*e) + 6*d^2*f*e^(4*I*f*x + 4*I*e) + 4*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-(64*a^6*c^5 - 320*I*a^6*c^4*d - 640*a^6*c^3*d^2 + 640*I*a^6*c^2*d^3 + 320*a^6*c*d^4 - 64*I*a^6*d^5)/f^2)*log(1/4*(8*a^3*c^3 - 16*I*a^3*c^2*d - 8*a^3*c*d^2 - (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(64*a^6*c^5 - 320*I*a^6*c^4*d - 640*a^6*c^3*d^2 + 640*I*a^6*c^2*d^3 + 320*a^6*c*d^4 - 64*I*a^6*d^5)/f^2) + (8*a^3*c^3 - 24*I*a^3*c^2*d - 24*a^3*c*d^2 + 8*I*a^3*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a^3*c^2 - 2*I*a^3*c*d - a^3*d^2)) - (80*I*a^3*c^4 - 1040*a^3*c^3*d + 12816*I*a^3*c^2*d^2 + 18608*a^3*c*d^3 - 7936*I*a^3*d^4 + (80*I*a^3*c^4 - 1120*a^3*c^3*d + 19296*I*a^3*c^2*d^2 + 34912*a^3*c*d^3 - 16816*I*a^3*d^4)*e^(8*I*f*x + 8*I*e) + (320*I*a^3*c^4 - 4400*a^3*c^3*d + 68304*I*a^3*c^2*d^2 + 107344*a^3*c*d^3 - 43760*I*a^3*d^4)*e^(6*I*f*x + 6*I*e) + (480*I*a^3*c^4 - 6480*a^3*c^3*d + 91536*I*a^3*c^2*d^2 + 134640*a^3*c*d^3 - 58128*I*a^3*d^4)*e^(4*I*f*x + 4*I*e) + (320*I*a^3*c^4 - 4240*a^3*c^3*d + 55344*I*a^3*c^2*d^2 + 80816*a^3*c*d^3 - 34640*I*a^3*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(8*I*f*x + 8*I*e) + 4*d^2*f*e^(6*I*f*x + 6*I*e) + 6*d^2*f*e^(4*I*f*x + 4*I*e) + 4*d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)","B",0
1114,1,924,0,0.828681," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{105 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 \, a^{4} c^{5} - 80 i \, a^{4} c^{4} d - 160 \, a^{4} c^{3} d^{2} + 160 i \, a^{4} c^{2} d^{3} + 80 \, a^{4} c d^{4} - 16 i \, a^{4} d^{5}}{f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c^{3} - 8 i \, a^{2} c^{2} d - 4 \, a^{2} c d^{2} - {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 \, a^{4} c^{5} - 80 i \, a^{4} c^{4} d - 160 \, a^{4} c^{3} d^{2} + 160 i \, a^{4} c^{2} d^{3} + 80 \, a^{4} c d^{4} - 16 i \, a^{4} d^{5}}{f^{2}}} + {\left(4 \, a^{2} c^{3} - 12 i \, a^{2} c^{2} d - 12 \, a^{2} c d^{2} + 4 i \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)}}\right) - 105 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{16 \, a^{4} c^{5} - 80 i \, a^{4} c^{4} d - 160 \, a^{4} c^{3} d^{2} + 160 i \, a^{4} c^{2} d^{3} + 80 \, a^{4} c d^{4} - 16 i \, a^{4} d^{5}}{f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c^{3} - 8 i \, a^{2} c^{2} d - 4 \, a^{2} c d^{2} - {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{16 \, a^{4} c^{5} - 80 i \, a^{4} c^{4} d - 160 \, a^{4} c^{3} d^{2} + 160 i \, a^{4} c^{2} d^{3} + 80 \, a^{4} c d^{4} - 16 i \, a^{4} d^{5}}{f^{2}}} + {\left(4 \, a^{2} c^{3} - 12 i \, a^{2} c^{2} d - 12 \, a^{2} c d^{2} + 4 i \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)}}\right) + {\left(120 \, a^{2} c^{3} - 2216 i \, a^{2} c^{2} d - 3048 \, a^{2} c d^{2} + 1336 i \, a^{2} d^{3} + {\left(120 \, a^{2} c^{3} - 2936 i \, a^{2} c^{2} d - 5512 \, a^{2} c d^{2} + 2696 i \, a^{2} d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(360 \, a^{2} c^{3} - 8088 i \, a^{2} c^{2} d - 12632 \, a^{2} c d^{2} + 4904 i \, a^{2} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(360 \, a^{2} c^{3} - 7368 i \, a^{2} c^{2} d - 10168 \, a^{2} c d^{2} + 4504 i \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{420 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"-1/420*(105*(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(16*a^4*c^5 - 80*I*a^4*c^4*d - 160*a^4*c^3*d^2 + 160*I*a^4*c^2*d^3 + 80*a^4*c*d^4 - 16*I*a^4*d^5)/f^2)*log(1/2*(4*a^2*c^3 - 8*I*a^2*c^2*d - 4*a^2*c*d^2 - (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(16*a^4*c^5 - 80*I*a^4*c^4*d - 160*a^4*c^3*d^2 + 160*I*a^4*c^2*d^3 + 80*a^4*c*d^4 - 16*I*a^4*d^5)/f^2) + (4*a^2*c^3 - 12*I*a^2*c^2*d - 12*a^2*c*d^2 + 4*I*a^2*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)) - 105*(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(16*a^4*c^5 - 80*I*a^4*c^4*d - 160*a^4*c^3*d^2 + 160*I*a^4*c^2*d^3 + 80*a^4*c*d^4 - 16*I*a^4*d^5)/f^2)*log(1/2*(4*a^2*c^3 - 8*I*a^2*c^2*d - 4*a^2*c*d^2 - (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(16*a^4*c^5 - 80*I*a^4*c^4*d - 160*a^4*c^3*d^2 + 160*I*a^4*c^2*d^3 + 80*a^4*c*d^4 - 16*I*a^4*d^5)/f^2) + (4*a^2*c^3 - 12*I*a^2*c^2*d - 12*a^2*c*d^2 + 4*I*a^2*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)) + (120*a^2*c^3 - 2216*I*a^2*c^2*d - 3048*a^2*c*d^2 + 1336*I*a^2*d^3 + (120*a^2*c^3 - 2936*I*a^2*c^2*d - 5512*a^2*c*d^2 + 2696*I*a^2*d^3)*e^(6*I*f*x + 6*I*e) + (360*a^2*c^3 - 8088*I*a^2*c^2*d - 12632*a^2*c*d^2 + 4904*I*a^2*d^3)*e^(4*I*f*x + 4*I*e) + (360*a^2*c^3 - 7368*I*a^2*c^2*d - 10168*a^2*c*d^2 + 4504*I*a^2*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
1115,1,736,0,0.692884," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{4 \, a^{2} c^{5} - 20 i \, a^{2} c^{4} d - 40 \, a^{2} c^{3} d^{2} + 40 i \, a^{2} c^{2} d^{3} + 20 \, a^{2} c d^{4} - 4 i \, a^{2} d^{5}}{f^{2}}} \log\left(\frac{{\left(2 \, a c^{3} - 4 i \, a c^{2} d - 2 \, a c d^{2} - {\left(i \, f e^{\left(2 i \, f x + 2 i \, e\right)} + i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, a^{2} c^{5} - 20 i \, a^{2} c^{4} d - 40 \, a^{2} c^{3} d^{2} + 40 i \, a^{2} c^{2} d^{3} + 20 \, a^{2} c d^{4} - 4 i \, a^{2} d^{5}}{f^{2}}} + {\left(2 \, a c^{3} - 6 i \, a c^{2} d - 6 \, a c d^{2} + 2 i \, a d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a c^{2} - 2 i \, a c d - a d^{2}}\right) - 15 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{4 \, a^{2} c^{5} - 20 i \, a^{2} c^{4} d - 40 \, a^{2} c^{3} d^{2} + 40 i \, a^{2} c^{2} d^{3} + 20 \, a^{2} c d^{4} - 4 i \, a^{2} d^{5}}{f^{2}}} \log\left(\frac{{\left(2 \, a c^{3} - 4 i \, a c^{2} d - 2 \, a c d^{2} - {\left(-i \, f e^{\left(2 i \, f x + 2 i \, e\right)} - i \, f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, a^{2} c^{5} - 20 i \, a^{2} c^{4} d - 40 \, a^{2} c^{3} d^{2} + 40 i \, a^{2} c^{2} d^{3} + 20 \, a^{2} c d^{4} - 4 i \, a^{2} d^{5}}{f^{2}}} + {\left(2 \, a c^{3} - 6 i \, a c^{2} d - 6 \, a c d^{2} + 2 i \, a d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a c^{2} - 2 i \, a c d - a d^{2}}\right) - {\left(184 i \, a c^{2} + 192 \, a c d - 104 i \, a d^{2} + {\left(184 i \, a c^{2} + 368 \, a c d - 184 i \, a d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(368 i \, a c^{2} + 560 \, a c d - 192 i \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{60 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"-1/60*(15*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(4*a^2*c^5 - 20*I*a^2*c^4*d - 40*a^2*c^3*d^2 + 40*I*a^2*c^2*d^3 + 20*a^2*c*d^4 - 4*I*a^2*d^5)/f^2)*log((2*a*c^3 - 4*I*a*c^2*d - 2*a*c*d^2 - (I*f*e^(2*I*f*x + 2*I*e) + I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*a^2*c^5 - 20*I*a^2*c^4*d - 40*a^2*c^3*d^2 + 40*I*a^2*c^2*d^3 + 20*a^2*c*d^4 - 4*I*a^2*d^5)/f^2) + (2*a*c^3 - 6*I*a*c^2*d - 6*a*c*d^2 + 2*I*a*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*c^2 - 2*I*a*c*d - a*d^2)) - 15*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(4*a^2*c^5 - 20*I*a^2*c^4*d - 40*a^2*c^3*d^2 + 40*I*a^2*c^2*d^3 + 20*a^2*c*d^4 - 4*I*a^2*d^5)/f^2)*log((2*a*c^3 - 4*I*a*c^2*d - 2*a*c*d^2 - (-I*f*e^(2*I*f*x + 2*I*e) - I*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*a^2*c^5 - 20*I*a^2*c^4*d - 40*a^2*c^3*d^2 + 40*I*a^2*c^2*d^3 + 20*a^2*c*d^4 - 4*I*a^2*d^5)/f^2) + (2*a*c^3 - 6*I*a*c^2*d - 6*a*c*d^2 + 2*I*a*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*c^2 - 2*I*a*c*d - a*d^2)) - (184*I*a*c^2 + 192*a*c*d - 104*I*a*d^2 + (184*I*a*c^2 + 368*a*c*d - 184*I*a*d^2)*e^(4*I*f*x + 4*I*e) + (368*I*a*c^2 + 560*a*c*d - 192*I*a*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1116,1,1037,0,0.830537," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(4 \, c^{3} - 8 i \, c^{2} d - 4 \, c d^{2} - {\left(4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{2} f^{2}}} + 2 \, {\left(2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(c^{2} - 2 i \, c d - d^{2}\right)}}\right) - a f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(4 \, c^{3} - 8 i \, c^{2} d - 4 \, c d^{2} - {\left(-4 i \, a f e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{2} f^{2}}} + 2 \, {\left(2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(c^{2} - 2 i \, c d - d^{2}\right)}}\right) - a f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d + 5 \, c^{3} d^{2} - 25 i \, c^{2} d^{3} + 40 \, c d^{4} + 16 i \, d^{5}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, c^{3} + 2 \, c^{2} d + 7 i \, c d^{2} - 4 \, d^{3} + {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d + 5 \, c^{3} d^{2} - 25 i \, c^{2} d^{3} + 40 \, c d^{4} + 16 i \, d^{5}}{a^{2} f^{2}}} + {\left(i \, c^{3} + 3 \, c^{2} d + 4 i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a f}\right) + a f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d + 5 \, c^{3} d^{2} - 25 i \, c^{2} d^{3} + 40 \, c d^{4} + 16 i \, d^{5}}{a^{2} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(\frac{{\left(i \, c^{3} + 2 \, c^{2} d + 7 i \, c d^{2} - 4 \, d^{3} - {\left(a f e^{\left(2 i \, f x + 2 i \, e\right)} + a f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d + 5 \, c^{3} d^{2} - 25 i \, c^{2} d^{3} + 40 \, c d^{4} + 16 i \, d^{5}}{a^{2} f^{2}}} + {\left(i \, c^{3} + 3 \, c^{2} d + 4 i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a f}\right) - 2 \, {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + {\left(i \, c^{2} - 2 \, c d - 9 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a f}"," ",0,"-1/8*(a*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(4*c^3 - 8*I*c^2*d - 4*c*d^2 - (4*I*a*f*e^(2*I*f*x + 2*I*e) + 4*I*a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^2*f^2)) + 2*(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(c^2 - 2*I*c*d - d^2)) - a*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(4*c^3 - 8*I*c^2*d - 4*c*d^2 - (-4*I*a*f*e^(2*I*f*x + 2*I*e) - 4*I*a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^2*f^2)) + 2*(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(c^2 - 2*I*c*d - d^2)) - a*f*sqrt(-(c^5 - 5*I*c^4*d + 5*c^3*d^2 - 25*I*c^2*d^3 + 40*c*d^4 + 16*I*d^5)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(I*c^3 + 2*c^2*d + 7*I*c*d^2 - 4*d^3 + (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d + 5*c^3*d^2 - 25*I*c^2*d^3 + 40*c*d^4 + 16*I*d^5)/(a^2*f^2)) + (I*c^3 + 3*c^2*d + 4*I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f)) + a*f*sqrt(-(c^5 - 5*I*c^4*d + 5*c^3*d^2 - 25*I*c^2*d^3 + 40*c*d^4 + 16*I*d^5)/(a^2*f^2))*e^(2*I*f*x + 2*I*e)*log(1/2*(I*c^3 + 2*c^2*d + 7*I*c*d^2 - 4*d^3 - (a*f*e^(2*I*f*x + 2*I*e) + a*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d + 5*c^3*d^2 - 25*I*c^2*d^3 + 40*c*d^4 + 16*I*d^5)/(a^2*f^2)) + (I*c^3 + 3*c^2*d + 4*I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f)) - 2*(I*c^2 - 2*c*d - I*d^2 + (I*c^2 - 2*c*d - 9*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-2*I*f*x - 2*I*e)/(a*f)","B",0
1117,1,1094,0,0.734529," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(8 \, c^{3} - 16 i \, c^{2} d - 8 \, c d^{2} - {\left(8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{4} f^{2}}} + 4 \, {\left(2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(c^{2} - 2 i \, c d - d^{2}\right)}}\right) - 2 \, a^{2} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(8 \, c^{3} - 16 i \, c^{2} d - 8 \, c d^{2} - {\left(-8 i \, a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{4} f^{2}}} + 4 \, {\left(2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(c^{2} - 2 i \, c d - d^{2}\right)}}\right) - a^{2} f \sqrt{-\frac{4 \, c^{5} - 20 i \, c^{4} d - 40 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} - 35 \, c d^{4} + 49 i \, d^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{3} + 4 \, c^{2} d - i \, c d^{2} + 7 \, d^{3} + {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, c^{5} - 20 i \, c^{4} d - 40 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} - 35 \, c d^{4} + 49 i \, d^{5}}{a^{4} f^{2}}} + {\left(2 i \, c^{3} + 6 \, c^{2} d - 7 i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) + a^{2} f \sqrt{-\frac{4 \, c^{5} - 20 i \, c^{4} d - 40 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} - 35 \, c d^{4} + 49 i \, d^{5}}{a^{4} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{3} + 4 \, c^{2} d - i \, c d^{2} + 7 \, d^{3} - {\left(a^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 \, c^{5} - 20 i \, c^{4} d - 40 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} - 35 \, c d^{4} + 49 i \, d^{5}}{a^{4} f^{2}}} + {\left(2 i \, c^{3} + 6 \, c^{2} d - 7 i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, a^{2} f}\right) - 2 \, {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + {\left(3 i \, c^{2} + 3 \, c d + 6 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 i \, c^{2} + c d + 5 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{32 \, a^{2} f}"," ",0,"-1/32*(2*a^2*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*(8*c^3 - 16*I*c^2*d - 8*c*d^2 - (8*I*a^2*f*e^(2*I*f*x + 2*I*e) + 8*I*a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^4*f^2)) + 4*(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(c^2 - 2*I*c*d - d^2)) - 2*a^2*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/4*(8*c^3 - 16*I*c^2*d - 8*c*d^2 - (-8*I*a^2*f*e^(2*I*f*x + 2*I*e) - 8*I*a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^4*f^2)) + 4*(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(c^2 - 2*I*c*d - d^2)) - a^2*f*sqrt(-(4*c^5 - 20*I*c^4*d - 40*c^3*d^2 + 20*I*c^2*d^3 - 35*c*d^4 + 49*I*d^5)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(2*I*c^3 + 4*c^2*d - I*c*d^2 + 7*d^3 + (a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*c^5 - 20*I*c^4*d - 40*c^3*d^2 + 20*I*c^2*d^3 - 35*c*d^4 + 49*I*d^5)/(a^4*f^2)) + (2*I*c^3 + 6*c^2*d - 7*I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) + a^2*f*sqrt(-(4*c^5 - 20*I*c^4*d - 40*c^3*d^2 + 20*I*c^2*d^3 - 35*c*d^4 + 49*I*d^5)/(a^4*f^2))*e^(4*I*f*x + 4*I*e)*log(1/8*(2*I*c^3 + 4*c^2*d - I*c*d^2 + 7*d^3 - (a^2*f*e^(2*I*f*x + 2*I*e) + a^2*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*c^5 - 20*I*c^4*d - 40*c^3*d^2 + 20*I*c^2*d^3 - 35*c*d^4 + 49*I*d^5)/(a^4*f^2)) + (2*I*c^3 + 6*c^2*d - 7*I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(a^2*f)) - 2*(I*c^2 - 2*c*d - I*d^2 + (3*I*c^2 + 3*c*d + 6*I*d^2)*e^(4*I*f*x + 4*I*e) + (4*I*c^2 + c*d + 5*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","B",0
1118,1,1264,0,1.019383," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{3} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(16 \, c^{3} - 32 i \, c^{2} d - 16 \, c d^{2} - {\left(16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{6} f^{2}}} + 8 \, {\left(2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, {\left(c^{2} - 2 i \, c d - d^{2}\right)}}\right) - 6 \, a^{3} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{6} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(16 \, c^{3} - 32 i \, c^{2} d - 16 \, c d^{2} - {\left(-16 i \, a^{3} f e^{\left(2 i \, f x + 2 i \, e\right)} - 16 i \, a^{3} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{6} f^{2}}} + 8 \, {\left(2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{8 \, {\left(c^{2} - 2 i \, c d - d^{2}\right)}}\right) - 3 \, a^{3} f \sqrt{-\frac{4 i \, c^{6} + 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} - 4 \, c d^{5} - 4 i \, d^{6}}{{\left(i \, a^{6} c - a^{6} d\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{4} - 2 i \, c^{3} d + 3 \, c^{2} d^{2} - 3 i \, c d^{3} + 2 \, d^{4} - {\left({\left(i \, a^{3} c - a^{3} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a^{3} c - a^{3} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, c^{6} + 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} - 4 \, c d^{5} - 4 i \, d^{6}}{{\left(i \, a^{6} c - a^{6} d\right)} f^{2}}} + {\left(2 \, c^{4} - 4 i \, c^{3} d - c^{2} d^{2} - 2 i \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{16 \, {\left(i \, a^{3} c - a^{3} d\right)} f}\right) + 3 \, a^{3} f \sqrt{-\frac{4 i \, c^{6} + 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} - 4 \, c d^{5} - 4 i \, d^{6}}{{\left(i \, a^{6} c - a^{6} d\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{4} - 2 i \, c^{3} d + 3 \, c^{2} d^{2} - 3 i \, c d^{3} + 2 \, d^{4} - {\left({\left(-i \, a^{3} c + a^{3} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a^{3} c + a^{3} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, c^{6} + 16 \, c^{5} d - 20 i \, c^{4} d^{2} - 15 i \, c^{2} d^{4} - 4 \, c d^{5} - 4 i \, d^{6}}{{\left(i \, a^{6} c - a^{6} d\right)} f^{2}}} + {\left(2 \, c^{4} - 4 i \, c^{3} d - c^{2} d^{2} - 2 i \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{16 \, {\left(i \, a^{3} c - a^{3} d\right)} f}\right) - 2 \, {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + {\left(11 i \, c^{2} + 18 \, c d - 4 i \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(18 i \, c^{2} + 17 \, c d + 2 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 i \, c^{2} - 5 \, c d + 4 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{192 \, a^{3} f}"," ",0,"-1/192*(6*a^3*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(16*c^3 - 32*I*c^2*d - 16*c*d^2 - (16*I*a^3*f*e^(2*I*f*x + 2*I*e) + 16*I*a^3*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^6*f^2)) + 8*(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(c^2 - 2*I*c*d - d^2)) - 6*a^3*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^6*f^2))*e^(6*I*f*x + 6*I*e)*log(1/8*(16*c^3 - 32*I*c^2*d - 16*c*d^2 - (-16*I*a^3*f*e^(2*I*f*x + 2*I*e) - 16*I*a^3*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^6*f^2)) + 8*(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/(c^2 - 2*I*c*d - d^2)) - 3*a^3*f*sqrt(-(4*I*c^6 + 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 - 4*c*d^5 - 4*I*d^6)/((I*a^6*c - a^6*d)*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/16*(2*c^4 - 2*I*c^3*d + 3*c^2*d^2 - 3*I*c*d^3 + 2*d^4 - ((I*a^3*c - a^3*d)*f*e^(2*I*f*x + 2*I*e) + (I*a^3*c - a^3*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*I*c^6 + 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 - 4*c*d^5 - 4*I*d^6)/((I*a^6*c - a^6*d)*f^2)) + (2*c^4 - 4*I*c^3*d - c^2*d^2 - 2*I*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((I*a^3*c - a^3*d)*f)) + 3*a^3*f*sqrt(-(4*I*c^6 + 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 - 4*c*d^5 - 4*I*d^6)/((I*a^6*c - a^6*d)*f^2))*e^(6*I*f*x + 6*I*e)*log(-1/16*(2*c^4 - 2*I*c^3*d + 3*c^2*d^2 - 3*I*c*d^3 + 2*d^4 - ((-I*a^3*c + a^3*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a^3*c + a^3*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-(4*I*c^6 + 16*c^5*d - 20*I*c^4*d^2 - 15*I*c^2*d^4 - 4*c*d^5 - 4*I*d^6)/((I*a^6*c - a^6*d)*f^2)) + (2*c^4 - 4*I*c^3*d - c^2*d^2 - 2*I*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((I*a^3*c - a^3*d)*f)) - 2*(2*I*c^2 - 4*c*d - 2*I*d^2 + (11*I*c^2 + 18*c*d - 4*I*d^2)*e^(6*I*f*x + 6*I*e) + (18*I*c^2 + 17*c*d + 2*I*d^2)*e^(4*I*f*x + 4*I*e) + (9*I*c^2 - 5*c*d + 4*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","B",0
1119,1,427,0,0.509798," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c + d\right)} f^{2}}} \log\left(\frac{{\left(8 \, a^{3} c + \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c + d\right)} f^{2}}} {\left({\left(i \, c + d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c + d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - 3 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)} \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c + d\right)} f^{2}}} \log\left(\frac{{\left(8 \, a^{3} c + \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c + d\right)} f^{2}}} {\left({\left(-i \, c - d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c - d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) + {\left(16 i \, a^{3} c - 64 \, a^{3} d - 16 \, {\left(-i \, a^{3} c + 5 \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{12 \, {\left(d^{2} f e^{\left(2 i \, f x + 2 i \, e\right)} + d^{2} f\right)}}"," ",0,"1/12*(3*(d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-64*I*a^6/((I*c + d)*f^2))*log(1/4*(8*a^3*c + sqrt(-64*I*a^6/((I*c + d)*f^2))*((I*c + d)*f*e^(2*I*f*x + 2*I*e) + (I*c + d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) - 3*(d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)*sqrt(-64*I*a^6/((I*c + d)*f^2))*log(1/4*(8*a^3*c + sqrt(-64*I*a^6/((I*c + d)*f^2))*((-I*c - d)*f*e^(2*I*f*x + 2*I*e) + (-I*c - d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) + (16*I*a^3*c - 64*a^3*d - 16*(-I*a^3*c + 5*a^3*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d^2*f*e^(2*I*f*x + 2*I*e) + d^2*f)","B",0
1120,1,341,0,0.445136," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{d \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c + d\right)} f^{2}}} f \log\left(\frac{{\left(4 \, a^{2} c + {\left({\left(i \, c + d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c + d\right)} f\right)} \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c + d\right)} f^{2}}} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - d \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c + d\right)} f^{2}}} f \log\left(\frac{{\left(4 \, a^{2} c + {\left({\left(-i \, c - d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c - d\right)} f\right)} \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c + d\right)} f^{2}}} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - 8 \, a^{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, d f}"," ",0,"1/4*(d*sqrt(-16*I*a^4/((I*c + d)*f^2))*f*log(1/2*(4*a^2*c + ((I*c + d)*f*e^(2*I*f*x + 2*I*e) + (I*c + d)*f)*sqrt(-16*I*a^4/((I*c + d)*f^2))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) - d*sqrt(-16*I*a^4/((I*c + d)*f^2))*f*log(1/2*(4*a^2*c + ((-I*c - d)*f*e^(2*I*f*x + 2*I*e) + (-I*c - d)*f)*sqrt(-16*I*a^4/((I*c + d)*f^2))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) - 8*a^2*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(d*f)","B",0
1121,1,275,0,0.460381," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c + d\right)} f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left({\left(i \, c + d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c + d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c + d\right)} f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - \frac{1}{4} \, \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c + d\right)} f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left({\left(-i \, c - d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c - d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c + d\right)} f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right)"," ",0,"1/4*sqrt(-4*I*a^2/((I*c + d)*f^2))*log((2*a*c + ((I*c + d)*f*e^(2*I*f*x + 2*I*e) + (I*c + d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/((I*c + d)*f^2)) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) - 1/4*sqrt(-4*I*a^2/((I*c + d)*f^2))*log((2*a*c + ((-I*c - d)*f*e^(2*I*f*x + 2*I*e) + (-I*c - d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/((I*c + d)*f^2)) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a)","B",0
1122,1,984,0,0.548396," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left({\left(i \, a c - a d\right)} f \sqrt{\frac{i}{4 \, {\left(-i \, a^{2} c - a^{2} d\right)} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-2 \, {\left(2 \, {\left({\left(i \, a c + a d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a c + a d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{4 \, {\left(-i \, a^{2} c - a^{2} d\right)} f^{2}}} - {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left(-i \, a c + a d\right)} f \sqrt{\frac{i}{4 \, {\left(-i \, a^{2} c - a^{2} d\right)} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-2 \, {\left(2 \, {\left({\left(-i \, a c - a d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a c - a d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{4 \, {\left(-i \, a^{2} c - a^{2} d\right)} f^{2}}} - {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left(i \, a c - a d\right)} f \sqrt{\frac{-i \, c^{2} + 4 \, c d + 4 i \, d^{2}}{{\left(4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d - 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(-i \, c^{2} + 3 \, c d + 2 i \, d^{2} + 2 \, {\left({\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-i \, c^{2} + 4 \, c d + 4 i \, d^{2}}{{\left(4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d - 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} + {\left(-i \, c^{2} + 2 \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} f}\right) + {\left(-i \, a c + a d\right)} f \sqrt{\frac{-i \, c^{2} + 4 \, c d + 4 i \, d^{2}}{{\left(4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d - 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(-\frac{{\left(-i \, c^{2} + 3 \, c d + 2 i \, d^{2} - 2 \, {\left({\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-i \, c^{2} + 4 \, c d + 4 i \, d^{2}}{{\left(4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d - 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} + {\left(-i \, c^{2} + 2 \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, {\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} f}\right) + \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, {\left(i \, a c - a d\right)} f}"," ",0,"-1/4*((I*a*c - a*d)*f*sqrt(1/4*I/((-I*a^2*c - a^2*d)*f^2))*e^(2*I*f*x + 2*I*e)*log(-2*(2*((I*a*c + a*d)*f*e^(2*I*f*x + 2*I*e) + (I*a*c + a*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/4*I/((-I*a^2*c - a^2*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) + (-I*a*c + a*d)*f*sqrt(1/4*I/((-I*a^2*c - a^2*d)*f^2))*e^(2*I*f*x + 2*I*e)*log(-2*(2*((-I*a*c - a*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a*c - a*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/4*I/((-I*a^2*c - a^2*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) + (I*a*c - a*d)*f*sqrt((-I*c^2 + 4*c*d + 4*I*d^2)/((4*I*a^2*c^3 - 12*a^2*c^2*d - 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/2*(-I*c^2 + 3*c*d + 2*I*d^2 + 2*((a*c^2 + 2*I*a*c*d - a*d^2)*f*e^(2*I*f*x + 2*I*e) + (a*c^2 + 2*I*a*c*d - a*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-I*c^2 + 4*c*d + 4*I*d^2)/((4*I*a^2*c^3 - 12*a^2*c^2*d - 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2)) + (-I*c^2 + 2*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a*c^2 + 2*I*a*c*d - a*d^2)*f)) + (-I*a*c + a*d)*f*sqrt((-I*c^2 + 4*c*d + 4*I*d^2)/((4*I*a^2*c^3 - 12*a^2*c^2*d - 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2))*e^(2*I*f*x + 2*I*e)*log(-1/2*(-I*c^2 + 3*c*d + 2*I*d^2 - 2*((a*c^2 + 2*I*a*c*d - a*d^2)*f*e^(2*I*f*x + 2*I*e) + (a*c^2 + 2*I*a*c*d - a*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-I*c^2 + 4*c*d + 4*I*d^2)/((4*I*a^2*c^3 - 12*a^2*c^2*d - 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2)) + (-I*c^2 + 2*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((a*c^2 + 2*I*a*c*d - a*d^2)*f)) + sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-2*I*f*x - 2*I*e)/((I*a*c - a*d)*f)","B",0
1123,1,1396,0,0.808335," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(4 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f \sqrt{\frac{i}{16 \, {\left(-i \, a^{4} c - a^{4} d\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-2 \, {\left(4 \, {\left({\left(i \, a^{2} c + a^{2} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a^{2} c + a^{2} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{16 \, {\left(-i \, a^{4} c - a^{4} d\right)} f^{2}}} - {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f \sqrt{\frac{i}{16 \, {\left(-i \, a^{4} c - a^{4} d\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-2 \, {\left(4 \, {\left({\left(-i \, a^{2} c - a^{2} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a^{2} c - a^{2} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{16 \, {\left(-i \, a^{4} c - a^{4} d\right)} f^{2}}} - {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 4 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f \sqrt{\frac{4 i \, c^{4} - 24 \, c^{3} d - 64 i \, c^{2} d^{2} + 84 \, c d^{3} + 49 i \, d^{4}}{{\left(-64 i \, a^{4} c^{5} + 320 \, a^{4} c^{4} d + 640 i \, a^{4} c^{3} d^{2} - 640 \, a^{4} c^{2} d^{3} - 320 i \, a^{4} c d^{4} + 64 \, a^{4} d^{5}\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{3} + 8 i \, c^{2} d - 13 \, c d^{2} - 7 i \, d^{3} - {\left({\left(8 i \, a^{2} c^{3} - 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, a^{2} c^{3} - 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{4} - 24 \, c^{3} d - 64 i \, c^{2} d^{2} + 84 \, c d^{3} + 49 i \, d^{4}}{{\left(-64 i \, a^{4} c^{5} + 320 \, a^{4} c^{4} d + 640 i \, a^{4} c^{3} d^{2} - 640 \, a^{4} c^{2} d^{3} - 320 i \, a^{4} c d^{4} + 64 \, a^{4} d^{5}\right)} f^{2}}} + {\left(2 \, c^{3} + 6 i \, c^{2} d - 7 \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(8 i \, a^{2} c^{3} - 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} f}\right) + 4 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f \sqrt{\frac{4 i \, c^{4} - 24 \, c^{3} d - 64 i \, c^{2} d^{2} + 84 \, c d^{3} + 49 i \, d^{4}}{{\left(-64 i \, a^{4} c^{5} + 320 \, a^{4} c^{4} d + 640 i \, a^{4} c^{3} d^{2} - 640 \, a^{4} c^{2} d^{3} - 320 i \, a^{4} c d^{4} + 64 \, a^{4} d^{5}\right)} f^{2}}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(-\frac{{\left(2 \, c^{3} + 8 i \, c^{2} d - 13 \, c d^{2} - 7 i \, d^{3} - {\left({\left(-8 i \, a^{2} c^{3} + 24 \, a^{2} c^{2} d + 24 i \, a^{2} c d^{2} - 8 \, a^{2} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, a^{2} c^{3} + 24 \, a^{2} c^{2} d + 24 i \, a^{2} c d^{2} - 8 \, a^{2} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{4} - 24 \, c^{3} d - 64 i \, c^{2} d^{2} + 84 \, c d^{3} + 49 i \, d^{4}}{{\left(-64 i \, a^{4} c^{5} + 320 \, a^{4} c^{4} d + 640 i \, a^{4} c^{3} d^{2} - 640 \, a^{4} c^{2} d^{3} - 320 i \, a^{4} c d^{4} + 64 \, a^{4} d^{5}\right)} f^{2}}} + {\left(2 \, c^{3} + 6 i \, c^{2} d - 7 \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(8 i \, a^{2} c^{3} - 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} f}\right) + {\left({\left(-3 i \, c + 6 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, c + 7 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{16 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f}"," ",0,"-1/16*(4*(a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*sqrt(1/16*I/((-I*a^4*c - a^4*d)*f^2))*e^(4*I*f*x + 4*I*e)*log(-2*(4*((I*a^2*c + a^2*d)*f*e^(2*I*f*x + 2*I*e) + (I*a^2*c + a^2*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I/((-I*a^4*c - a^4*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) - 4*(a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*sqrt(1/16*I/((-I*a^4*c - a^4*d)*f^2))*e^(4*I*f*x + 4*I*e)*log(-2*(4*((-I*a^2*c - a^2*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a^2*c - a^2*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/16*I/((-I*a^4*c - a^4*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) - 4*(a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*sqrt((4*I*c^4 - 24*c^3*d - 64*I*c^2*d^2 + 84*c*d^3 + 49*I*d^4)/((-64*I*a^4*c^5 + 320*a^4*c^4*d + 640*I*a^4*c^3*d^2 - 640*a^4*c^2*d^3 - 320*I*a^4*c*d^4 + 64*a^4*d^5)*f^2))*e^(4*I*f*x + 4*I*e)*log(-(2*c^3 + 8*I*c^2*d - 13*c*d^2 - 7*I*d^3 - ((8*I*a^2*c^3 - 24*a^2*c^2*d - 24*I*a^2*c*d^2 + 8*a^2*d^3)*f*e^(2*I*f*x + 2*I*e) + (8*I*a^2*c^3 - 24*a^2*c^2*d - 24*I*a^2*c*d^2 + 8*a^2*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^4 - 24*c^3*d - 64*I*c^2*d^2 + 84*c*d^3 + 49*I*d^4)/((-64*I*a^4*c^5 + 320*a^4*c^4*d + 640*I*a^4*c^3*d^2 - 640*a^4*c^2*d^3 - 320*I*a^4*c*d^4 + 64*a^4*d^5)*f^2)) + (2*c^3 + 6*I*c^2*d - 7*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((8*I*a^2*c^3 - 24*a^2*c^2*d - 24*I*a^2*c*d^2 + 8*a^2*d^3)*f)) + 4*(a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*sqrt((4*I*c^4 - 24*c^3*d - 64*I*c^2*d^2 + 84*c*d^3 + 49*I*d^4)/((-64*I*a^4*c^5 + 320*a^4*c^4*d + 640*I*a^4*c^3*d^2 - 640*a^4*c^2*d^3 - 320*I*a^4*c*d^4 + 64*a^4*d^5)*f^2))*e^(4*I*f*x + 4*I*e)*log(-(2*c^3 + 8*I*c^2*d - 13*c*d^2 - 7*I*d^3 - ((-8*I*a^2*c^3 + 24*a^2*c^2*d + 24*I*a^2*c*d^2 - 8*a^2*d^3)*f*e^(2*I*f*x + 2*I*e) + (-8*I*a^2*c^3 + 24*a^2*c^2*d + 24*I*a^2*c*d^2 - 8*a^2*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^4 - 24*c^3*d - 64*I*c^2*d^2 + 84*c*d^3 + 49*I*d^4)/((-64*I*a^4*c^5 + 320*a^4*c^4*d + 640*I*a^4*c^3*d^2 - 640*a^4*c^2*d^3 - 320*I*a^4*c*d^4 + 64*a^4*d^5)*f^2)) + (2*c^3 + 6*I*c^2*d - 7*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((8*I*a^2*c^3 - 24*a^2*c^2*d - 24*I*a^2*c*d^2 + 8*a^2*d^3)*f)) + ((-3*I*c + 6*d)*e^(4*I*f*x + 4*I*e) + (-4*I*c + 7*d)*e^(2*I*f*x + 2*I*e) - I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-4*I*f*x - 4*I*e)/((a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f)","B",0
1124,1,1750,0,1.041712," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(-24 i \, a^{3} c^{3} + 72 \, a^{3} c^{2} d + 72 i \, a^{3} c d^{2} - 24 \, a^{3} d^{3}\right)} f \sqrt{\frac{i}{64 \, {\left(-i \, a^{6} c - a^{6} d\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-2 \, {\left(8 \, {\left({\left(i \, a^{3} c + a^{3} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a^{3} c + a^{3} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{64 \, {\left(-i \, a^{6} c - a^{6} d\right)} f^{2}}} - {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left(24 i \, a^{3} c^{3} - 72 \, a^{3} c^{2} d - 72 i \, a^{3} c d^{2} + 24 \, a^{3} d^{3}\right)} f \sqrt{\frac{i}{64 \, {\left(-i \, a^{6} c - a^{6} d\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-2 \, {\left(8 \, {\left({\left(-i \, a^{3} c - a^{3} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a^{3} c - a^{3} d\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{64 \, {\left(-i \, a^{6} c - a^{6} d\right)} f^{2}}} - {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left(24 i \, a^{3} c^{3} - 72 \, a^{3} c^{2} d - 72 i \, a^{3} c d^{2} + 24 \, a^{3} d^{3}\right)} f \sqrt{\frac{-4 i \, c^{6} + 32 \, c^{5} d + 116 i \, c^{4} d^{2} - 256 \, c^{3} d^{3} - 361 i \, c^{2} d^{4} + 312 \, c d^{5} + 144 i \, d^{6}}{{\left(256 i \, a^{6} c^{7} - 1792 \, a^{6} c^{6} d - 5376 i \, a^{6} c^{5} d^{2} + 8960 \, a^{6} c^{4} d^{3} + 8960 i \, a^{6} c^{3} d^{4} - 5376 \, a^{6} c^{2} d^{5} - 1792 i \, a^{6} c d^{6} + 256 \, a^{6} d^{7}\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{4} - 10 \, c^{3} d - 21 i \, c^{2} d^{2} + 25 \, c d^{3} + 12 i \, d^{4} + {\left({\left(16 \, a^{3} c^{4} + 64 i \, a^{3} c^{3} d - 96 \, a^{3} c^{2} d^{2} - 64 i \, a^{3} c d^{3} + 16 \, a^{3} d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 \, a^{3} c^{4} + 64 i \, a^{3} c^{3} d - 96 \, a^{3} c^{2} d^{2} - 64 i \, a^{3} c d^{3} + 16 \, a^{3} d^{4}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{6} + 32 \, c^{5} d + 116 i \, c^{4} d^{2} - 256 \, c^{3} d^{3} - 361 i \, c^{2} d^{4} + 312 \, c d^{5} + 144 i \, d^{6}}{{\left(256 i \, a^{6} c^{7} - 1792 \, a^{6} c^{6} d - 5376 i \, a^{6} c^{5} d^{2} + 8960 \, a^{6} c^{4} d^{3} + 8960 i \, a^{6} c^{3} d^{4} - 5376 \, a^{6} c^{2} d^{5} - 1792 i \, a^{6} c d^{6} + 256 \, a^{6} d^{7}\right)} f^{2}}} + {\left(2 i \, c^{4} - 8 \, c^{3} d - 13 i \, c^{2} d^{2} + 12 \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(16 \, a^{3} c^{4} + 64 i \, a^{3} c^{3} d - 96 \, a^{3} c^{2} d^{2} - 64 i \, a^{3} c d^{3} + 16 \, a^{3} d^{4}\right)} f}\right) + {\left(-24 i \, a^{3} c^{3} + 72 \, a^{3} c^{2} d + 72 i \, a^{3} c d^{2} - 24 \, a^{3} d^{3}\right)} f \sqrt{\frac{-4 i \, c^{6} + 32 \, c^{5} d + 116 i \, c^{4} d^{2} - 256 \, c^{3} d^{3} - 361 i \, c^{2} d^{4} + 312 \, c d^{5} + 144 i \, d^{6}}{{\left(256 i \, a^{6} c^{7} - 1792 \, a^{6} c^{6} d - 5376 i \, a^{6} c^{5} d^{2} + 8960 \, a^{6} c^{4} d^{3} + 8960 i \, a^{6} c^{3} d^{4} - 5376 \, a^{6} c^{2} d^{5} - 1792 i \, a^{6} c d^{6} + 256 \, a^{6} d^{7}\right)} f^{2}}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{{\left(2 i \, c^{4} - 10 \, c^{3} d - 21 i \, c^{2} d^{2} + 25 \, c d^{3} + 12 i \, d^{4} - {\left({\left(16 \, a^{3} c^{4} + 64 i \, a^{3} c^{3} d - 96 \, a^{3} c^{2} d^{2} - 64 i \, a^{3} c d^{3} + 16 \, a^{3} d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 \, a^{3} c^{4} + 64 i \, a^{3} c^{3} d - 96 \, a^{3} c^{2} d^{2} - 64 i \, a^{3} c d^{3} + 16 \, a^{3} d^{4}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{6} + 32 \, c^{5} d + 116 i \, c^{4} d^{2} - 256 \, c^{3} d^{3} - 361 i \, c^{2} d^{4} + 312 \, c d^{5} + 144 i \, d^{6}}{{\left(256 i \, a^{6} c^{7} - 1792 \, a^{6} c^{6} d - 5376 i \, a^{6} c^{5} d^{2} + 8960 \, a^{6} c^{4} d^{3} + 8960 i \, a^{6} c^{3} d^{4} - 5376 \, a^{6} c^{2} d^{5} - 1792 i \, a^{6} c d^{6} + 256 \, a^{6} d^{7}\right)} f^{2}}} + {\left(2 i \, c^{4} - 8 \, c^{3} d - 13 i \, c^{2} d^{2} + 12 \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(16 \, a^{3} c^{4} + 64 i \, a^{3} c^{3} d - 96 \, a^{3} c^{2} d^{2} - 64 i \, a^{3} c d^{3} + 16 \, a^{3} d^{4}\right)} f}\right) - {\left(2 \, c^{2} + 4 i \, c d - 2 \, d^{2} + {\left(11 \, c^{2} + 36 i \, c d - 40 \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(18 \, c^{2} + 55 i \, c d - 52 \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 \, c^{2} + 23 i \, c d - 14 \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{{\left(96 i \, a^{3} c^{3} - 288 \, a^{3} c^{2} d - 288 i \, a^{3} c d^{2} + 96 \, a^{3} d^{3}\right)} f}"," ",0,"((-24*I*a^3*c^3 + 72*a^3*c^2*d + 72*I*a^3*c*d^2 - 24*a^3*d^3)*f*sqrt(1/64*I/((-I*a^6*c - a^6*d)*f^2))*e^(6*I*f*x + 6*I*e)*log(-2*(8*((I*a^3*c + a^3*d)*f*e^(2*I*f*x + 2*I*e) + (I*a^3*c + a^3*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I/((-I*a^6*c - a^6*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) + (24*I*a^3*c^3 - 72*a^3*c^2*d - 72*I*a^3*c*d^2 + 24*a^3*d^3)*f*sqrt(1/64*I/((-I*a^6*c - a^6*d)*f^2))*e^(6*I*f*x + 6*I*e)*log(-2*(8*((-I*a^3*c - a^3*d)*f*e^(2*I*f*x + 2*I*e) + (-I*a^3*c - a^3*d)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(1/64*I/((-I*a^6*c - a^6*d)*f^2)) - (c - I*d)*e^(2*I*f*x + 2*I*e) - c)*e^(-2*I*f*x - 2*I*e)) + (24*I*a^3*c^3 - 72*a^3*c^2*d - 72*I*a^3*c*d^2 + 24*a^3*d^3)*f*sqrt((-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4 + 312*c*d^5 + 144*I*d^6)/((256*I*a^6*c^7 - 1792*a^6*c^6*d - 5376*I*a^6*c^5*d^2 + 8960*a^6*c^4*d^3 + 8960*I*a^6*c^3*d^4 - 5376*a^6*c^2*d^5 - 1792*I*a^6*c*d^6 + 256*a^6*d^7)*f^2))*e^(6*I*f*x + 6*I*e)*log((2*I*c^4 - 10*c^3*d - 21*I*c^2*d^2 + 25*c*d^3 + 12*I*d^4 + ((16*a^3*c^4 + 64*I*a^3*c^3*d - 96*a^3*c^2*d^2 - 64*I*a^3*c*d^3 + 16*a^3*d^4)*f*e^(2*I*f*x + 2*I*e) + (16*a^3*c^4 + 64*I*a^3*c^3*d - 96*a^3*c^2*d^2 - 64*I*a^3*c*d^3 + 16*a^3*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4 + 312*c*d^5 + 144*I*d^6)/((256*I*a^6*c^7 - 1792*a^6*c^6*d - 5376*I*a^6*c^5*d^2 + 8960*a^6*c^4*d^3 + 8960*I*a^6*c^3*d^4 - 5376*a^6*c^2*d^5 - 1792*I*a^6*c*d^6 + 256*a^6*d^7)*f^2)) + (2*I*c^4 - 8*c^3*d - 13*I*c^2*d^2 + 12*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((16*a^3*c^4 + 64*I*a^3*c^3*d - 96*a^3*c^2*d^2 - 64*I*a^3*c*d^3 + 16*a^3*d^4)*f)) + (-24*I*a^3*c^3 + 72*a^3*c^2*d + 72*I*a^3*c*d^2 - 24*a^3*d^3)*f*sqrt((-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4 + 312*c*d^5 + 144*I*d^6)/((256*I*a^6*c^7 - 1792*a^6*c^6*d - 5376*I*a^6*c^5*d^2 + 8960*a^6*c^4*d^3 + 8960*I*a^6*c^3*d^4 - 5376*a^6*c^2*d^5 - 1792*I*a^6*c*d^6 + 256*a^6*d^7)*f^2))*e^(6*I*f*x + 6*I*e)*log((2*I*c^4 - 10*c^3*d - 21*I*c^2*d^2 + 25*c*d^3 + 12*I*d^4 - ((16*a^3*c^4 + 64*I*a^3*c^3*d - 96*a^3*c^2*d^2 - 64*I*a^3*c*d^3 + 16*a^3*d^4)*f*e^(2*I*f*x + 2*I*e) + (16*a^3*c^4 + 64*I*a^3*c^3*d - 96*a^3*c^2*d^2 - 64*I*a^3*c*d^3 + 16*a^3*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^6 + 32*c^5*d + 116*I*c^4*d^2 - 256*c^3*d^3 - 361*I*c^2*d^4 + 312*c*d^5 + 144*I*d^6)/((256*I*a^6*c^7 - 1792*a^6*c^6*d - 5376*I*a^6*c^5*d^2 + 8960*a^6*c^4*d^3 + 8960*I*a^6*c^3*d^4 - 5376*a^6*c^2*d^5 - 1792*I*a^6*c*d^6 + 256*a^6*d^7)*f^2)) + (2*I*c^4 - 8*c^3*d - 13*I*c^2*d^2 + 12*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((16*a^3*c^4 + 64*I*a^3*c^3*d - 96*a^3*c^2*d^2 - 64*I*a^3*c*d^3 + 16*a^3*d^4)*f)) - (2*c^2 + 4*I*c*d - 2*d^2 + (11*c^2 + 36*I*c*d - 40*d^2)*e^(6*I*f*x + 6*I*e) + (18*c^2 + 55*I*c*d - 52*d^2)*e^(4*I*f*x + 4*I*e) + (9*c^2 + 23*I*c*d - 14*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-6*I*f*x - 6*I*e)/((96*I*a^3*c^3 - 288*a^3*c^2*d - 288*I*a^3*c*d^2 + 96*a^3*d^3)*f)","B",0
1125,1,606,0,0.504764," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{64 i \, a^{6}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} {\left({\left(c^{2} d^{2} - 2 i \, c d^{3} - d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d^{2} + d^{4}\right)} f\right)} \log\left(\frac{{\left(8 \, a^{3} c + \sqrt{\frac{64 i \, a^{6}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} {\left({\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - \sqrt{\frac{64 i \, a^{6}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} {\left({\left(c^{2} d^{2} - 2 i \, c d^{3} - d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d^{2} + d^{4}\right)} f\right)} \log\left(\frac{{\left(8 \, a^{3} c + \sqrt{\frac{64 i \, a^{6}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} {\left({\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - {\left(16 i \, a^{3} c^{2} - 16 \, a^{3} c d + {\left(16 i \, a^{3} c^{2} - 16 i \, a^{3} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(4 \, c^{2} d^{2} - 8 i \, c d^{3} - 4 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, {\left(c^{2} d^{2} + d^{4}\right)} f}"," ",0,"(sqrt(64*I*a^6/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*((c^2*d^2 - 2*I*c*d^3 - d^4)*f*e^(2*I*f*x + 2*I*e) + (c^2*d^2 + d^4)*f)*log(1/4*(8*a^3*c + sqrt(64*I*a^6/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*((I*c^2 + 2*c*d - I*d^2)*f*e^(2*I*f*x + 2*I*e) + (I*c^2 + 2*c*d - I*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) - sqrt(64*I*a^6/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*((c^2*d^2 - 2*I*c*d^3 - d^4)*f*e^(2*I*f*x + 2*I*e) + (c^2*d^2 + d^4)*f)*log(1/4*(8*a^3*c + sqrt(64*I*a^6/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*((-I*c^2 - 2*c*d + I*d^2)*f*e^(2*I*f*x + 2*I*e) + (-I*c^2 - 2*c*d + I*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) - (16*I*a^3*c^2 - 16*a^3*c*d + (16*I*a^3*c^2 - 16*I*a^3*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((4*c^2*d^2 - 8*I*c*d^3 - 4*d^4)*f*e^(2*I*f*x + 2*I*e) + 4*(c^2*d^2 + d^4)*f)","B",0
1126,1,586,0,0.532699," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} d - 2 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d + d^{3}\right)} f\right)} \sqrt{\frac{16 i \, a^{4}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c + {\left({\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f\right)} \sqrt{\frac{16 i \, a^{4}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - {\left({\left(c^{2} d - 2 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d + d^{3}\right)} f\right)} \sqrt{\frac{16 i \, a^{4}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c + {\left({\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f\right)} \sqrt{\frac{16 i \, a^{4}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) + {\left(8 \, a^{2} c + 8 i \, a^{2} d + {\left(8 \, a^{2} c + 8 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(4 \, c^{2} d - 8 i \, c d^{2} - 4 \, d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, {\left(c^{2} d + d^{3}\right)} f}"," ",0,"(((c^2*d - 2*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (c^2*d + d^3)*f)*sqrt(16*I*a^4/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(1/2*(4*a^2*c + ((I*c^2 + 2*c*d - I*d^2)*f*e^(2*I*f*x + 2*I*e) + (I*c^2 + 2*c*d - I*d^2)*f)*sqrt(16*I*a^4/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) - ((c^2*d - 2*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (c^2*d + d^3)*f)*sqrt(16*I*a^4/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(1/2*(4*a^2*c + ((-I*c^2 - 2*c*d + I*d^2)*f*e^(2*I*f*x + 2*I*e) + (-I*c^2 - 2*c*d + I*d^2)*f)*sqrt(16*I*a^4/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) + (8*a^2*c + 8*I*a^2*d + (8*a^2*c + 8*I*a^2*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((4*c^2*d - 8*I*c*d^2 - 4*d^3)*f*e^(2*I*f*x + 2*I*e) + 4*(c^2*d + d^3)*f)","B",0
1127,1,536,0,0.474921," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} - 2 i \, c d - d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} + d^{2}\right)} f\right)} \sqrt{\frac{4 i \, a^{2}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left({\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - {\left({\left(c^{2} - 2 i \, c d - d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} + d^{2}\right)} f\right)} \sqrt{\frac{4 i \, a^{2}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left({\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, a^{2}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - {\left(-8 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(4 \, c^{2} - 8 i \, c d - 4 \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 4 \, {\left(c^{2} + d^{2}\right)} f}"," ",0,"(((c^2 - 2*I*c*d - d^2)*f*e^(2*I*f*x + 2*I*e) + (c^2 + d^2)*f)*sqrt(4*I*a^2/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log((2*a*c + ((I*c^2 + 2*c*d - I*d^2)*f*e^(2*I*f*x + 2*I*e) + (I*c^2 + 2*c*d - I*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2)) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) - ((c^2 - 2*I*c*d - d^2)*f*e^(2*I*f*x + 2*I*e) + (c^2 + d^2)*f)*sqrt(4*I*a^2/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log((2*a*c + ((-I*c^2 - 2*c*d + I*d^2)*f*e^(2*I*f*x + 2*I*e) + (-I*c^2 - 2*c*d + I*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(4*I*a^2/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2)) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) - (-8*I*a*e^(2*I*f*x + 2*I*e) - 8*I*a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((4*c^2 - 8*I*c*d - 4*d^2)*f*e^(2*I*f*x + 2*I*e) + 4*(c^2 + d^2)*f)","B",0
1128,1,1549,0,0.941543," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(a c^{4} + 2 i \, a c^{3} d + 2 i \, a c d^{3} - a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d + 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} \log\left({\left({\left({\left(4 i \, a c^{2} + 8 \, a c d - 4 i \, a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, a c^{2} + 8 \, a c d - 4 i \, a d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{{\left(-4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d + 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left({\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(a c^{4} + 2 i \, a c^{3} d + 2 i \, a c d^{3} - a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d + 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} \log\left({\left({\left({\left(-4 i \, a c^{2} - 8 \, a c d + 4 i \, a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-4 i \, a c^{2} - 8 \, a c d + 4 i \, a d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{{\left(-4 i \, a^{2} c^{3} - 12 \, a^{2} c^{2} d + 12 i \, a^{2} c d^{2} + 4 \, a^{2} d^{3}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(a c^{4} + 2 i \, a c^{3} d + 2 i \, a c d^{3} - a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{i \, c^{2} - 8 \, c d - 16 i \, d^{2}}{{\left(-4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d + 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} - 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} \log\left(-\frac{{\left(c^{2} + 5 i \, c d - 4 \, d^{2} - {\left({\left(2 i \, a c^{3} - 6 \, a c^{2} d - 6 i \, a c d^{2} + 2 \, a d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, a c^{3} - 6 \, a c^{2} d - 6 i \, a c d^{2} + 2 \, a d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, c^{2} - 8 \, c d - 16 i \, d^{2}}{{\left(-4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d + 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} - 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} + {\left(c^{2} + 4 i \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(2 i \, a c^{3} - 6 \, a c^{2} d - 6 i \, a c d^{2} + 2 \, a d^{3}\right)} f}\right) - {\left({\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(a c^{4} + 2 i \, a c^{3} d + 2 i \, a c d^{3} - a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{i \, c^{2} - 8 \, c d - 16 i \, d^{2}}{{\left(-4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d + 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} - 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} \log\left(-\frac{{\left(c^{2} + 5 i \, c d - 4 \, d^{2} - {\left({\left(-2 i \, a c^{3} + 6 \, a c^{2} d + 6 i \, a c d^{2} - 2 \, a d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-2 i \, a c^{3} + 6 \, a c^{2} d + 6 i \, a c d^{2} - 2 \, a d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i \, c^{2} - 8 \, c d - 16 i \, d^{2}}{{\left(-4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d + 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} - 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} + {\left(c^{2} + 4 i \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(2 i \, a c^{3} - 6 \, a c^{2} d - 6 i \, a c d^{2} + 2 \, a d^{3}\right)} f}\right) + {\left(i \, c^{2} + i \, d^{2} + {\left(i \, c^{2} + 2 \, c d - 9 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, c^{2} + 2 \, c d - 8 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{4 \, {\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 \, a c^{4} + 8 i \, a c^{3} d + 8 i \, a c d^{3} - 4 \, a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(((a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(4*I*f*x + 4*I*e) + (a*c^4 + 2*I*a*c^3*d + 2*I*a*c*d^3 - a*d^4)*f*e^(2*I*f*x + 2*I*e))*sqrt(I/((-4*I*a^2*c^3 - 12*a^2*c^2*d + 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2))*log((((4*I*a*c^2 + 8*a*c*d - 4*I*a*d^2)*f*e^(2*I*f*x + 2*I*e) + (4*I*a*c^2 + 8*a*c*d - 4*I*a*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/((-4*I*a^2*c^3 - 12*a^2*c^2*d + 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) - ((a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(4*I*f*x + 4*I*e) + (a*c^4 + 2*I*a*c^3*d + 2*I*a*c*d^3 - a*d^4)*f*e^(2*I*f*x + 2*I*e))*sqrt(I/((-4*I*a^2*c^3 - 12*a^2*c^2*d + 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2))*log((((-4*I*a*c^2 - 8*a*c*d + 4*I*a*d^2)*f*e^(2*I*f*x + 2*I*e) + (-4*I*a*c^2 - 8*a*c*d + 4*I*a*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/((-4*I*a^2*c^3 - 12*a^2*c^2*d + 12*I*a^2*c*d^2 + 4*a^2*d^3)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(4*I*f*x + 4*I*e) + (a*c^4 + 2*I*a*c^3*d + 2*I*a*c*d^3 - a*d^4)*f*e^(2*I*f*x + 2*I*e))*sqrt((I*c^2 - 8*c*d - 16*I*d^2)/((-4*I*a^2*c^5 + 20*a^2*c^4*d + 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 - 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2))*log(-(c^2 + 5*I*c*d - 4*d^2 - ((2*I*a*c^3 - 6*a*c^2*d - 6*I*a*c*d^2 + 2*a*d^3)*f*e^(2*I*f*x + 2*I*e) + (2*I*a*c^3 - 6*a*c^2*d - 6*I*a*c*d^2 + 2*a*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((I*c^2 - 8*c*d - 16*I*d^2)/((-4*I*a^2*c^5 + 20*a^2*c^4*d + 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 - 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2)) + (c^2 + 4*I*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((2*I*a*c^3 - 6*a*c^2*d - 6*I*a*c*d^2 + 2*a*d^3)*f)) - ((a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(4*I*f*x + 4*I*e) + (a*c^4 + 2*I*a*c^3*d + 2*I*a*c*d^3 - a*d^4)*f*e^(2*I*f*x + 2*I*e))*sqrt((I*c^2 - 8*c*d - 16*I*d^2)/((-4*I*a^2*c^5 + 20*a^2*c^4*d + 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 - 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2))*log(-(c^2 + 5*I*c*d - 4*d^2 - ((-2*I*a*c^3 + 6*a*c^2*d + 6*I*a*c*d^2 - 2*a*d^3)*f*e^(2*I*f*x + 2*I*e) + (-2*I*a*c^3 + 6*a*c^2*d + 6*I*a*c*d^2 - 2*a*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((I*c^2 - 8*c*d - 16*I*d^2)/((-4*I*a^2*c^5 + 20*a^2*c^4*d + 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 - 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2)) + (c^2 + 4*I*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((2*I*a*c^3 - 6*a*c^2*d - 6*I*a*c*d^2 + 2*a*d^3)*f)) + (I*c^2 + I*d^2 + (I*c^2 + 2*c*d - 9*I*d^2)*e^(4*I*f*x + 4*I*e) + (2*I*c^2 + 2*c*d - 8*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(4*(a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(4*I*f*x + 4*I*e) + (4*a*c^4 + 8*I*a*c^3*d + 8*I*a*c*d^3 - 4*a*d^4)*f*e^(2*I*f*x + 2*I*e))","B",0
1129,1,2270,0,1.828969," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(-4 i \, a^{2} c^{5} + 4 \, a^{2} c^{4} d - 8 i \, a^{2} c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3} - 4 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-4 i \, a^{2} c^{5} + 12 \, a^{2} c^{4} d + 8 i \, a^{2} c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3} + 12 i \, a^{2} c d^{4} - 4 \, a^{2} d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-16 i \, a^{4} c^{3} - 48 \, a^{4} c^{2} d + 48 i \, a^{4} c d^{2} + 16 \, a^{4} d^{3}\right)} f^{2}}} \log\left({\left({\left({\left(8 i \, a^{2} c^{2} + 16 \, a^{2} c d - 8 i \, a^{2} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, a^{2} c^{2} + 16 \, a^{2} c d - 8 i \, a^{2} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{{\left(-16 i \, a^{4} c^{3} - 48 \, a^{4} c^{2} d + 48 i \, a^{4} c d^{2} + 16 \, a^{4} d^{3}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(4 i \, a^{2} c^{5} - 4 \, a^{2} c^{4} d + 8 i \, a^{2} c^{3} d^{2} - 8 \, a^{2} c^{2} d^{3} + 4 i \, a^{2} c d^{4} - 4 \, a^{2} d^{5}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(4 i \, a^{2} c^{5} - 12 \, a^{2} c^{4} d - 8 i \, a^{2} c^{3} d^{2} - 8 \, a^{2} c^{2} d^{3} - 12 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-16 i \, a^{4} c^{3} - 48 \, a^{4} c^{2} d + 48 i \, a^{4} c d^{2} + 16 \, a^{4} d^{3}\right)} f^{2}}} \log\left({\left({\left({\left(-8 i \, a^{2} c^{2} - 16 \, a^{2} c d + 8 i \, a^{2} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, a^{2} c^{2} - 16 \, a^{2} c d + 8 i \, a^{2} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{{\left(-16 i \, a^{4} c^{3} - 48 \, a^{4} c^{2} d + 48 i \, a^{4} c d^{2} + 16 \, a^{4} d^{3}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(-4 i \, a^{2} c^{5} + 4 \, a^{2} c^{4} d - 8 i \, a^{2} c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3} - 4 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-4 i \, a^{2} c^{5} + 12 \, a^{2} c^{4} d + 8 i \, a^{2} c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3} + 12 i \, a^{2} c d^{4} - 4 \, a^{2} d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{-4 i \, c^{4} + 40 \, c^{3} d + 192 i \, c^{2} d^{2} - 460 \, c d^{3} - 529 i \, d^{4}}{{\left(64 i \, a^{4} c^{7} - 448 \, a^{4} c^{6} d - 1344 i \, a^{4} c^{5} d^{2} + 2240 \, a^{4} c^{4} d^{3} + 2240 i \, a^{4} c^{3} d^{4} - 1344 \, a^{4} c^{2} d^{5} - 448 i \, a^{4} c d^{6} + 64 \, a^{4} d^{7}\right)} f^{2}}} \log\left(\frac{{\left(2 i \, c^{3} - 12 \, c^{2} d - 33 i \, c d^{2} + 23 \, d^{3} + {\left({\left(8 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d - 48 \, a^{2} c^{2} d^{2} - 32 i \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d - 48 \, a^{2} c^{2} d^{2} - 32 i \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{4} + 40 \, c^{3} d + 192 i \, c^{2} d^{2} - 460 \, c d^{3} - 529 i \, d^{4}}{{\left(64 i \, a^{4} c^{7} - 448 \, a^{4} c^{6} d - 1344 i \, a^{4} c^{5} d^{2} + 2240 \, a^{4} c^{4} d^{3} + 2240 i \, a^{4} c^{3} d^{4} - 1344 \, a^{4} c^{2} d^{5} - 448 i \, a^{4} c d^{6} + 64 \, a^{4} d^{7}\right)} f^{2}}} + {\left(2 i \, c^{3} - 10 \, c^{2} d - 23 i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(8 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d - 48 \, a^{2} c^{2} d^{2} - 32 i \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} f}\right) + {\left({\left(4 i \, a^{2} c^{5} - 4 \, a^{2} c^{4} d + 8 i \, a^{2} c^{3} d^{2} - 8 \, a^{2} c^{2} d^{3} + 4 i \, a^{2} c d^{4} - 4 \, a^{2} d^{5}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(4 i \, a^{2} c^{5} - 12 \, a^{2} c^{4} d - 8 i \, a^{2} c^{3} d^{2} - 8 \, a^{2} c^{2} d^{3} - 12 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{-4 i \, c^{4} + 40 \, c^{3} d + 192 i \, c^{2} d^{2} - 460 \, c d^{3} - 529 i \, d^{4}}{{\left(64 i \, a^{4} c^{7} - 448 \, a^{4} c^{6} d - 1344 i \, a^{4} c^{5} d^{2} + 2240 \, a^{4} c^{4} d^{3} + 2240 i \, a^{4} c^{3} d^{4} - 1344 \, a^{4} c^{2} d^{5} - 448 i \, a^{4} c d^{6} + 64 \, a^{4} d^{7}\right)} f^{2}}} \log\left(\frac{{\left(2 i \, c^{3} - 12 \, c^{2} d - 33 i \, c d^{2} + 23 \, d^{3} - {\left({\left(8 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d - 48 \, a^{2} c^{2} d^{2} - 32 i \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d - 48 \, a^{2} c^{2} d^{2} - 32 i \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{4} + 40 \, c^{3} d + 192 i \, c^{2} d^{2} - 460 \, c d^{3} - 529 i \, d^{4}}{{\left(64 i \, a^{4} c^{7} - 448 \, a^{4} c^{6} d - 1344 i \, a^{4} c^{5} d^{2} + 2240 \, a^{4} c^{4} d^{3} + 2240 i \, a^{4} c^{3} d^{4} - 1344 \, a^{4} c^{2} d^{5} - 448 i \, a^{4} c d^{6} + 64 \, a^{4} d^{7}\right)} f^{2}}} + {\left(2 i \, c^{3} - 10 \, c^{2} d - 23 i \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(8 \, a^{2} c^{4} + 32 i \, a^{2} c^{3} d - 48 \, a^{2} c^{2} d^{2} - 32 i \, a^{2} c d^{3} + 8 \, a^{2} d^{4}\right)} f}\right) + {\left(c^{3} + i \, c^{2} d + c d^{2} + i \, d^{3} + {\left(3 \, c^{3} + 4 i \, c^{2} d + 17 \, c d^{2} - 42 i \, d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(7 \, c^{3} + 13 i \, c^{2} d + 21 \, c d^{2} - 33 i \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(5 \, c^{3} + 10 i \, c^{2} d + 5 \, c d^{2} + 10 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(-16 i \, a^{2} c^{5} + 16 \, a^{2} c^{4} d - 32 i \, a^{2} c^{3} d^{2} + 32 \, a^{2} c^{2} d^{3} - 16 i \, a^{2} c d^{4} + 16 \, a^{2} d^{5}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-16 i \, a^{2} c^{5} + 48 \, a^{2} c^{4} d + 32 i \, a^{2} c^{3} d^{2} + 32 \, a^{2} c^{2} d^{3} + 48 i \, a^{2} c d^{4} - 16 \, a^{2} d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}}"," ",0,"(((-4*I*a^2*c^5 + 4*a^2*c^4*d - 8*I*a^2*c^3*d^2 + 8*a^2*c^2*d^3 - 4*I*a^2*c*d^4 + 4*a^2*d^5)*f*e^(6*I*f*x + 6*I*e) + (-4*I*a^2*c^5 + 12*a^2*c^4*d + 8*I*a^2*c^3*d^2 + 8*a^2*c^2*d^3 + 12*I*a^2*c*d^4 - 4*a^2*d^5)*f*e^(4*I*f*x + 4*I*e))*sqrt(I/((-16*I*a^4*c^3 - 48*a^4*c^2*d + 48*I*a^4*c*d^2 + 16*a^4*d^3)*f^2))*log((((8*I*a^2*c^2 + 16*a^2*c*d - 8*I*a^2*d^2)*f*e^(2*I*f*x + 2*I*e) + (8*I*a^2*c^2 + 16*a^2*c*d - 8*I*a^2*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/((-16*I*a^4*c^3 - 48*a^4*c^2*d + 48*I*a^4*c*d^2 + 16*a^4*d^3)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((4*I*a^2*c^5 - 4*a^2*c^4*d + 8*I*a^2*c^3*d^2 - 8*a^2*c^2*d^3 + 4*I*a^2*c*d^4 - 4*a^2*d^5)*f*e^(6*I*f*x + 6*I*e) + (4*I*a^2*c^5 - 12*a^2*c^4*d - 8*I*a^2*c^3*d^2 - 8*a^2*c^2*d^3 - 12*I*a^2*c*d^4 + 4*a^2*d^5)*f*e^(4*I*f*x + 4*I*e))*sqrt(I/((-16*I*a^4*c^3 - 48*a^4*c^2*d + 48*I*a^4*c*d^2 + 16*a^4*d^3)*f^2))*log((((-8*I*a^2*c^2 - 16*a^2*c*d + 8*I*a^2*d^2)*f*e^(2*I*f*x + 2*I*e) + (-8*I*a^2*c^2 - 16*a^2*c*d + 8*I*a^2*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/((-16*I*a^4*c^3 - 48*a^4*c^2*d + 48*I*a^4*c*d^2 + 16*a^4*d^3)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((-4*I*a^2*c^5 + 4*a^2*c^4*d - 8*I*a^2*c^3*d^2 + 8*a^2*c^2*d^3 - 4*I*a^2*c*d^4 + 4*a^2*d^5)*f*e^(6*I*f*x + 6*I*e) + (-4*I*a^2*c^5 + 12*a^2*c^4*d + 8*I*a^2*c^3*d^2 + 8*a^2*c^2*d^3 + 12*I*a^2*c*d^4 - 4*a^2*d^5)*f*e^(4*I*f*x + 4*I*e))*sqrt((-4*I*c^4 + 40*c^3*d + 192*I*c^2*d^2 - 460*c*d^3 - 529*I*d^4)/((64*I*a^4*c^7 - 448*a^4*c^6*d - 1344*I*a^4*c^5*d^2 + 2240*a^4*c^4*d^3 + 2240*I*a^4*c^3*d^4 - 1344*a^4*c^2*d^5 - 448*I*a^4*c*d^6 + 64*a^4*d^7)*f^2))*log((2*I*c^3 - 12*c^2*d - 33*I*c*d^2 + 23*d^3 + ((8*a^2*c^4 + 32*I*a^2*c^3*d - 48*a^2*c^2*d^2 - 32*I*a^2*c*d^3 + 8*a^2*d^4)*f*e^(2*I*f*x + 2*I*e) + (8*a^2*c^4 + 32*I*a^2*c^3*d - 48*a^2*c^2*d^2 - 32*I*a^2*c*d^3 + 8*a^2*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^4 + 40*c^3*d + 192*I*c^2*d^2 - 460*c*d^3 - 529*I*d^4)/((64*I*a^4*c^7 - 448*a^4*c^6*d - 1344*I*a^4*c^5*d^2 + 2240*a^4*c^4*d^3 + 2240*I*a^4*c^3*d^4 - 1344*a^4*c^2*d^5 - 448*I*a^4*c*d^6 + 64*a^4*d^7)*f^2)) + (2*I*c^3 - 10*c^2*d - 23*I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((8*a^2*c^4 + 32*I*a^2*c^3*d - 48*a^2*c^2*d^2 - 32*I*a^2*c*d^3 + 8*a^2*d^4)*f)) + ((4*I*a^2*c^5 - 4*a^2*c^4*d + 8*I*a^2*c^3*d^2 - 8*a^2*c^2*d^3 + 4*I*a^2*c*d^4 - 4*a^2*d^5)*f*e^(6*I*f*x + 6*I*e) + (4*I*a^2*c^5 - 12*a^2*c^4*d - 8*I*a^2*c^3*d^2 - 8*a^2*c^2*d^3 - 12*I*a^2*c*d^4 + 4*a^2*d^5)*f*e^(4*I*f*x + 4*I*e))*sqrt((-4*I*c^4 + 40*c^3*d + 192*I*c^2*d^2 - 460*c*d^3 - 529*I*d^4)/((64*I*a^4*c^7 - 448*a^4*c^6*d - 1344*I*a^4*c^5*d^2 + 2240*a^4*c^4*d^3 + 2240*I*a^4*c^3*d^4 - 1344*a^4*c^2*d^5 - 448*I*a^4*c*d^6 + 64*a^4*d^7)*f^2))*log((2*I*c^3 - 12*c^2*d - 33*I*c*d^2 + 23*d^3 - ((8*a^2*c^4 + 32*I*a^2*c^3*d - 48*a^2*c^2*d^2 - 32*I*a^2*c*d^3 + 8*a^2*d^4)*f*e^(2*I*f*x + 2*I*e) + (8*a^2*c^4 + 32*I*a^2*c^3*d - 48*a^2*c^2*d^2 - 32*I*a^2*c*d^3 + 8*a^2*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^4 + 40*c^3*d + 192*I*c^2*d^2 - 460*c*d^3 - 529*I*d^4)/((64*I*a^4*c^7 - 448*a^4*c^6*d - 1344*I*a^4*c^5*d^2 + 2240*a^4*c^4*d^3 + 2240*I*a^4*c^3*d^4 - 1344*a^4*c^2*d^5 - 448*I*a^4*c*d^6 + 64*a^4*d^7)*f^2)) + (2*I*c^3 - 10*c^2*d - 23*I*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((8*a^2*c^4 + 32*I*a^2*c^3*d - 48*a^2*c^2*d^2 - 32*I*a^2*c*d^3 + 8*a^2*d^4)*f)) + (c^3 + I*c^2*d + c*d^2 + I*d^3 + (3*c^3 + 4*I*c^2*d + 17*c*d^2 - 42*I*d^3)*e^(6*I*f*x + 6*I*e) + (7*c^3 + 13*I*c^2*d + 21*c*d^2 - 33*I*d^3)*e^(4*I*f*x + 4*I*e) + (5*c^3 + 10*I*c^2*d + 5*c*d^2 + 10*I*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((-16*I*a^2*c^5 + 16*a^2*c^4*d - 32*I*a^2*c^3*d^2 + 32*a^2*c^2*d^3 - 16*I*a^2*c*d^4 + 16*a^2*d^5)*f*e^(6*I*f*x + 6*I*e) + (-16*I*a^2*c^5 + 48*a^2*c^4*d + 32*I*a^2*c^3*d^2 + 32*a^2*c^2*d^3 + 48*I*a^2*c*d^4 - 16*a^2*d^5)*f*e^(4*I*f*x + 4*I*e))","B",0
1130,1,2645,0,5.174733," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(24 \, a^{3} c^{6} + 48 i \, a^{3} c^{5} d + 24 \, a^{3} c^{4} d^{2} + 96 i \, a^{3} c^{3} d^{3} - 24 \, a^{3} c^{2} d^{4} + 48 i \, a^{3} c d^{5} - 24 \, a^{3} d^{6}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 120 \, a^{3} c^{4} d^{2} - 120 \, a^{3} c^{2} d^{4} - 96 i \, a^{3} c d^{5} + 24 \, a^{3} d^{6}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-64 i \, a^{6} c^{3} - 192 \, a^{6} c^{2} d + 192 i \, a^{6} c d^{2} + 64 \, a^{6} d^{3}\right)} f^{2}}} \log\left({\left({\left({\left(16 i \, a^{3} c^{2} + 32 \, a^{3} c d - 16 i \, a^{3} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, a^{3} c^{2} + 32 \, a^{3} c d - 16 i \, a^{3} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{{\left(-64 i \, a^{6} c^{3} - 192 \, a^{6} c^{2} d + 192 i \, a^{6} c d^{2} + 64 \, a^{6} d^{3}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left({\left(24 \, a^{3} c^{6} + 48 i \, a^{3} c^{5} d + 24 \, a^{3} c^{4} d^{2} + 96 i \, a^{3} c^{3} d^{3} - 24 \, a^{3} c^{2} d^{4} + 48 i \, a^{3} c d^{5} - 24 \, a^{3} d^{6}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 120 \, a^{3} c^{4} d^{2} - 120 \, a^{3} c^{2} d^{4} - 96 i \, a^{3} c d^{5} + 24 \, a^{3} d^{6}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-64 i \, a^{6} c^{3} - 192 \, a^{6} c^{2} d + 192 i \, a^{6} c d^{2} + 64 \, a^{6} d^{3}\right)} f^{2}}} \log\left({\left({\left({\left(-16 i \, a^{3} c^{2} - 32 \, a^{3} c d + 16 i \, a^{3} d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-16 i \, a^{3} c^{2} - 32 \, a^{3} c d + 16 i \, a^{3} d^{2}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{i}{{\left(-64 i \, a^{6} c^{3} - 192 \, a^{6} c^{2} d + 192 i \, a^{6} c d^{2} + 64 \, a^{6} d^{3}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left({\left(24 \, a^{3} c^{6} + 48 i \, a^{3} c^{5} d + 24 \, a^{3} c^{4} d^{2} + 96 i \, a^{3} c^{3} d^{3} - 24 \, a^{3} c^{2} d^{4} + 48 i \, a^{3} c d^{5} - 24 \, a^{3} d^{6}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 120 \, a^{3} c^{4} d^{2} - 120 \, a^{3} c^{2} d^{4} - 96 i \, a^{3} c d^{5} + 24 \, a^{3} d^{6}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{4 i \, c^{6} - 48 \, c^{5} d - 276 i \, c^{4} d^{2} + 1024 \, c^{3} d^{3} + 2481 i \, c^{2} d^{4} - 3828 \, c d^{5} - 3364 i \, d^{6}}{{\left(-256 i \, a^{6} c^{9} + 2304 \, a^{6} c^{8} d + 9216 i \, a^{6} c^{7} d^{2} - 21504 \, a^{6} c^{6} d^{3} - 32256 i \, a^{6} c^{5} d^{4} + 32256 \, a^{6} c^{4} d^{5} + 21504 i \, a^{6} c^{3} d^{6} - 9216 \, a^{6} c^{2} d^{7} - 2304 i \, a^{6} c d^{8} + 256 \, a^{6} d^{9}\right)} f^{2}}} \log\left(\frac{{\left(2 \, c^{4} + 14 i \, c^{3} d - 45 \, c^{2} d^{2} - 91 i \, c d^{3} + 58 \, d^{4} + {\left({\left(16 i \, a^{3} c^{5} - 80 \, a^{3} c^{4} d - 160 i \, a^{3} c^{3} d^{2} + 160 \, a^{3} c^{2} d^{3} + 80 i \, a^{3} c d^{4} - 16 \, a^{3} d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, a^{3} c^{5} - 80 \, a^{3} c^{4} d - 160 i \, a^{3} c^{3} d^{2} + 160 \, a^{3} c^{2} d^{3} + 80 i \, a^{3} c d^{4} - 16 \, a^{3} d^{5}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{6} - 48 \, c^{5} d - 276 i \, c^{4} d^{2} + 1024 \, c^{3} d^{3} + 2481 i \, c^{2} d^{4} - 3828 \, c d^{5} - 3364 i \, d^{6}}{{\left(-256 i \, a^{6} c^{9} + 2304 \, a^{6} c^{8} d + 9216 i \, a^{6} c^{7} d^{2} - 21504 \, a^{6} c^{6} d^{3} - 32256 i \, a^{6} c^{5} d^{4} + 32256 \, a^{6} c^{4} d^{5} + 21504 i \, a^{6} c^{3} d^{6} - 9216 \, a^{6} c^{2} d^{7} - 2304 i \, a^{6} c d^{8} + 256 \, a^{6} d^{9}\right)} f^{2}}} + {\left(2 \, c^{4} + 12 i \, c^{3} d - 33 \, c^{2} d^{2} - 58 i \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(-16 i \, a^{3} c^{5} + 80 \, a^{3} c^{4} d + 160 i \, a^{3} c^{3} d^{2} - 160 \, a^{3} c^{2} d^{3} - 80 i \, a^{3} c d^{4} + 16 \, a^{3} d^{5}\right)} f}\right) + {\left({\left(24 \, a^{3} c^{6} + 48 i \, a^{3} c^{5} d + 24 \, a^{3} c^{4} d^{2} + 96 i \, a^{3} c^{3} d^{3} - 24 \, a^{3} c^{2} d^{4} + 48 i \, a^{3} c d^{5} - 24 \, a^{3} d^{6}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 120 \, a^{3} c^{4} d^{2} - 120 \, a^{3} c^{2} d^{4} - 96 i \, a^{3} c d^{5} + 24 \, a^{3} d^{6}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{4 i \, c^{6} - 48 \, c^{5} d - 276 i \, c^{4} d^{2} + 1024 \, c^{3} d^{3} + 2481 i \, c^{2} d^{4} - 3828 \, c d^{5} - 3364 i \, d^{6}}{{\left(-256 i \, a^{6} c^{9} + 2304 \, a^{6} c^{8} d + 9216 i \, a^{6} c^{7} d^{2} - 21504 \, a^{6} c^{6} d^{3} - 32256 i \, a^{6} c^{5} d^{4} + 32256 \, a^{6} c^{4} d^{5} + 21504 i \, a^{6} c^{3} d^{6} - 9216 \, a^{6} c^{2} d^{7} - 2304 i \, a^{6} c d^{8} + 256 \, a^{6} d^{9}\right)} f^{2}}} \log\left(\frac{{\left(2 \, c^{4} + 14 i \, c^{3} d - 45 \, c^{2} d^{2} - 91 i \, c d^{3} + 58 \, d^{4} + {\left({\left(-16 i \, a^{3} c^{5} + 80 \, a^{3} c^{4} d + 160 i \, a^{3} c^{3} d^{2} - 160 \, a^{3} c^{2} d^{3} - 80 i \, a^{3} c d^{4} + 16 \, a^{3} d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-16 i \, a^{3} c^{5} + 80 \, a^{3} c^{4} d + 160 i \, a^{3} c^{3} d^{2} - 160 \, a^{3} c^{2} d^{3} - 80 i \, a^{3} c d^{4} + 16 \, a^{3} d^{5}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{6} - 48 \, c^{5} d - 276 i \, c^{4} d^{2} + 1024 \, c^{3} d^{3} + 2481 i \, c^{2} d^{4} - 3828 \, c d^{5} - 3364 i \, d^{6}}{{\left(-256 i \, a^{6} c^{9} + 2304 \, a^{6} c^{8} d + 9216 i \, a^{6} c^{7} d^{2} - 21504 \, a^{6} c^{6} d^{3} - 32256 i \, a^{6} c^{5} d^{4} + 32256 \, a^{6} c^{4} d^{5} + 21504 i \, a^{6} c^{3} d^{6} - 9216 \, a^{6} c^{2} d^{7} - 2304 i \, a^{6} c d^{8} + 256 \, a^{6} d^{9}\right)} f^{2}}} + {\left(2 \, c^{4} + 12 i \, c^{3} d - 33 \, c^{2} d^{2} - 58 i \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(-16 i \, a^{3} c^{5} + 80 \, a^{3} c^{4} d + 160 i \, a^{3} c^{3} d^{2} - 160 \, a^{3} c^{2} d^{3} - 80 i \, a^{3} c d^{4} + 16 \, a^{3} d^{5}\right)} f}\right) - {\left(-2 i \, c^{4} + 4 \, c^{3} d + 4 \, c d^{3} + 2 i \, d^{4} + {\left(-11 i \, c^{4} + 32 \, c^{3} d + 3 i \, c^{2} d^{2} + 146 \, c d^{3} - 292 i \, d^{4}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-29 i \, c^{4} + 97 \, c^{3} d + 67 i \, c^{2} d^{2} + 211 \, c d^{3} - 210 i \, d^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-27 i \, c^{4} + 90 \, c^{3} d + 71 i \, c^{2} d^{2} + 90 \, c d^{3} + 98 i \, d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-11 i \, c^{4} + 29 \, c^{3} d + 7 i \, c^{2} d^{2} + 29 \, c d^{3} + 18 i \, d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(96 \, a^{3} c^{6} + 192 i \, a^{3} c^{5} d + 96 \, a^{3} c^{4} d^{2} + 384 i \, a^{3} c^{3} d^{3} - 96 \, a^{3} c^{2} d^{4} + 192 i \, a^{3} c d^{5} - 96 \, a^{3} d^{6}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(96 \, a^{3} c^{6} + 384 i \, a^{3} c^{5} d - 480 \, a^{3} c^{4} d^{2} - 480 \, a^{3} c^{2} d^{4} - 384 i \, a^{3} c d^{5} + 96 \, a^{3} d^{6}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}}"," ",0,"(((24*a^3*c^6 + 48*I*a^3*c^5*d + 24*a^3*c^4*d^2 + 96*I*a^3*c^3*d^3 - 24*a^3*c^2*d^4 + 48*I*a^3*c*d^5 - 24*a^3*d^6)*f*e^(8*I*f*x + 8*I*e) + (24*a^3*c^6 + 96*I*a^3*c^5*d - 120*a^3*c^4*d^2 - 120*a^3*c^2*d^4 - 96*I*a^3*c*d^5 + 24*a^3*d^6)*f*e^(6*I*f*x + 6*I*e))*sqrt(I/((-64*I*a^6*c^3 - 192*a^6*c^2*d + 192*I*a^6*c*d^2 + 64*a^6*d^3)*f^2))*log((((16*I*a^3*c^2 + 32*a^3*c*d - 16*I*a^3*d^2)*f*e^(2*I*f*x + 2*I*e) + (16*I*a^3*c^2 + 32*a^3*c*d - 16*I*a^3*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/((-64*I*a^6*c^3 - 192*a^6*c^2*d + 192*I*a^6*c*d^2 + 64*a^6*d^3)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) - ((24*a^3*c^6 + 48*I*a^3*c^5*d + 24*a^3*c^4*d^2 + 96*I*a^3*c^3*d^3 - 24*a^3*c^2*d^4 + 48*I*a^3*c*d^5 - 24*a^3*d^6)*f*e^(8*I*f*x + 8*I*e) + (24*a^3*c^6 + 96*I*a^3*c^5*d - 120*a^3*c^4*d^2 - 120*a^3*c^2*d^4 - 96*I*a^3*c*d^5 + 24*a^3*d^6)*f*e^(6*I*f*x + 6*I*e))*sqrt(I/((-64*I*a^6*c^3 - 192*a^6*c^2*d + 192*I*a^6*c*d^2 + 64*a^6*d^3)*f^2))*log((((-16*I*a^3*c^2 - 32*a^3*c*d + 16*I*a^3*d^2)*f*e^(2*I*f*x + 2*I*e) + (-16*I*a^3*c^2 - 32*a^3*c*d + 16*I*a^3*d^2)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(I/((-64*I*a^6*c^3 - 192*a^6*c^2*d + 192*I*a^6*c*d^2 + 64*a^6*d^3)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) - ((24*a^3*c^6 + 48*I*a^3*c^5*d + 24*a^3*c^4*d^2 + 96*I*a^3*c^3*d^3 - 24*a^3*c^2*d^4 + 48*I*a^3*c*d^5 - 24*a^3*d^6)*f*e^(8*I*f*x + 8*I*e) + (24*a^3*c^6 + 96*I*a^3*c^5*d - 120*a^3*c^4*d^2 - 120*a^3*c^2*d^4 - 96*I*a^3*c*d^5 + 24*a^3*d^6)*f*e^(6*I*f*x + 6*I*e))*sqrt((4*I*c^6 - 48*c^5*d - 276*I*c^4*d^2 + 1024*c^3*d^3 + 2481*I*c^2*d^4 - 3828*c*d^5 - 3364*I*d^6)/((-256*I*a^6*c^9 + 2304*a^6*c^8*d + 9216*I*a^6*c^7*d^2 - 21504*a^6*c^6*d^3 - 32256*I*a^6*c^5*d^4 + 32256*a^6*c^4*d^5 + 21504*I*a^6*c^3*d^6 - 9216*a^6*c^2*d^7 - 2304*I*a^6*c*d^8 + 256*a^6*d^9)*f^2))*log((2*c^4 + 14*I*c^3*d - 45*c^2*d^2 - 91*I*c*d^3 + 58*d^4 + ((16*I*a^3*c^5 - 80*a^3*c^4*d - 160*I*a^3*c^3*d^2 + 160*a^3*c^2*d^3 + 80*I*a^3*c*d^4 - 16*a^3*d^5)*f*e^(2*I*f*x + 2*I*e) + (16*I*a^3*c^5 - 80*a^3*c^4*d - 160*I*a^3*c^3*d^2 + 160*a^3*c^2*d^3 + 80*I*a^3*c*d^4 - 16*a^3*d^5)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^6 - 48*c^5*d - 276*I*c^4*d^2 + 1024*c^3*d^3 + 2481*I*c^2*d^4 - 3828*c*d^5 - 3364*I*d^6)/((-256*I*a^6*c^9 + 2304*a^6*c^8*d + 9216*I*a^6*c^7*d^2 - 21504*a^6*c^6*d^3 - 32256*I*a^6*c^5*d^4 + 32256*a^6*c^4*d^5 + 21504*I*a^6*c^3*d^6 - 9216*a^6*c^2*d^7 - 2304*I*a^6*c*d^8 + 256*a^6*d^9)*f^2)) + (2*c^4 + 12*I*c^3*d - 33*c^2*d^2 - 58*I*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((-16*I*a^3*c^5 + 80*a^3*c^4*d + 160*I*a^3*c^3*d^2 - 160*a^3*c^2*d^3 - 80*I*a^3*c*d^4 + 16*a^3*d^5)*f)) + ((24*a^3*c^6 + 48*I*a^3*c^5*d + 24*a^3*c^4*d^2 + 96*I*a^3*c^3*d^3 - 24*a^3*c^2*d^4 + 48*I*a^3*c*d^5 - 24*a^3*d^6)*f*e^(8*I*f*x + 8*I*e) + (24*a^3*c^6 + 96*I*a^3*c^5*d - 120*a^3*c^4*d^2 - 120*a^3*c^2*d^4 - 96*I*a^3*c*d^5 + 24*a^3*d^6)*f*e^(6*I*f*x + 6*I*e))*sqrt((4*I*c^6 - 48*c^5*d - 276*I*c^4*d^2 + 1024*c^3*d^3 + 2481*I*c^2*d^4 - 3828*c*d^5 - 3364*I*d^6)/((-256*I*a^6*c^9 + 2304*a^6*c^8*d + 9216*I*a^6*c^7*d^2 - 21504*a^6*c^6*d^3 - 32256*I*a^6*c^5*d^4 + 32256*a^6*c^4*d^5 + 21504*I*a^6*c^3*d^6 - 9216*a^6*c^2*d^7 - 2304*I*a^6*c*d^8 + 256*a^6*d^9)*f^2))*log((2*c^4 + 14*I*c^3*d - 45*c^2*d^2 - 91*I*c*d^3 + 58*d^4 + ((-16*I*a^3*c^5 + 80*a^3*c^4*d + 160*I*a^3*c^3*d^2 - 160*a^3*c^2*d^3 - 80*I*a^3*c*d^4 + 16*a^3*d^5)*f*e^(2*I*f*x + 2*I*e) + (-16*I*a^3*c^5 + 80*a^3*c^4*d + 160*I*a^3*c^3*d^2 - 160*a^3*c^2*d^3 - 80*I*a^3*c*d^4 + 16*a^3*d^5)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^6 - 48*c^5*d - 276*I*c^4*d^2 + 1024*c^3*d^3 + 2481*I*c^2*d^4 - 3828*c*d^5 - 3364*I*d^6)/((-256*I*a^6*c^9 + 2304*a^6*c^8*d + 9216*I*a^6*c^7*d^2 - 21504*a^6*c^6*d^3 - 32256*I*a^6*c^5*d^4 + 32256*a^6*c^4*d^5 + 21504*I*a^6*c^3*d^6 - 9216*a^6*c^2*d^7 - 2304*I*a^6*c*d^8 + 256*a^6*d^9)*f^2)) + (2*c^4 + 12*I*c^3*d - 33*c^2*d^2 - 58*I*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((-16*I*a^3*c^5 + 80*a^3*c^4*d + 160*I*a^3*c^3*d^2 - 160*a^3*c^2*d^3 - 80*I*a^3*c*d^4 + 16*a^3*d^5)*f)) - (-2*I*c^4 + 4*c^3*d + 4*c*d^3 + 2*I*d^4 + (-11*I*c^4 + 32*c^3*d + 3*I*c^2*d^2 + 146*c*d^3 - 292*I*d^4)*e^(8*I*f*x + 8*I*e) + (-29*I*c^4 + 97*c^3*d + 67*I*c^2*d^2 + 211*c*d^3 - 210*I*d^4)*e^(6*I*f*x + 6*I*e) + (-27*I*c^4 + 90*c^3*d + 71*I*c^2*d^2 + 90*c*d^3 + 98*I*d^4)*e^(4*I*f*x + 4*I*e) + (-11*I*c^4 + 29*c^3*d + 7*I*c^2*d^2 + 29*c*d^3 + 18*I*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((96*a^3*c^6 + 192*I*a^3*c^5*d + 96*a^3*c^4*d^2 + 384*I*a^3*c^3*d^3 - 96*a^3*c^2*d^4 + 192*I*a^3*c*d^5 - 96*a^3*d^6)*f*e^(8*I*f*x + 8*I*e) + (96*a^3*c^6 + 384*I*a^3*c^5*d - 480*a^3*c^4*d^2 - 480*a^3*c^2*d^4 - 384*I*a^3*c*d^5 + 96*a^3*d^6)*f*e^(6*I*f*x + 6*I*e))","B",0
1131,1,972,0,0.618985," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} {\left({\left(3 \, c^{4} d^{2} - 12 i \, c^{3} d^{3} - 18 \, c^{2} d^{4} + 12 i \, c d^{5} + 3 \, d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} d^{2} - 12 i \, c^{3} d^{3} - 12 i \, c d^{5} - 6 \, d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}\right)} f\right)} \log\left(\frac{{\left(8 \, a^{3} c + \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} {\left({\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) - \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} {\left({\left(3 \, c^{4} d^{2} - 12 i \, c^{3} d^{3} - 18 \, c^{2} d^{4} + 12 i \, c d^{5} + 3 \, d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} d^{2} - 12 i \, c^{3} d^{3} - 12 i \, c d^{5} - 6 \, d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}\right)} f\right)} \log\left(\frac{{\left(8 \, a^{3} c + \sqrt{-\frac{64 i \, a^{6}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} {\left({\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(8 \, a^{3} c - 8 i \, a^{3} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{4 \, a^{3}}\right) + {\left(16 i \, a^{3} c^{3} + 32 \, a^{3} c^{2} d + 112 i \, a^{3} c d^{2} - 64 \, a^{3} d^{3} + {\left(16 i \, a^{3} c^{3} + 80 \, a^{3} c^{2} d + 16 i \, a^{3} c d^{2} + 80 \, a^{3} d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(32 i \, a^{3} c^{3} + 112 \, a^{3} c^{2} d + 128 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(12 \, c^{4} d^{2} - 48 i \, c^{3} d^{3} - 72 \, c^{2} d^{4} + 48 i \, c d^{5} + 12 \, d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 \, c^{4} d^{2} - 48 i \, c^{3} d^{3} - 48 i \, c d^{5} - 24 \, d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 12 \, {\left(c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}\right)} f}"," ",0,"(sqrt(-64*I*a^6/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*((3*c^4*d^2 - 12*I*c^3*d^3 - 18*c^2*d^4 + 12*I*c*d^5 + 3*d^6)*f*e^(4*I*f*x + 4*I*e) + (6*c^4*d^2 - 12*I*c^3*d^3 - 12*I*c*d^5 - 6*d^6)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4*d^2 + 2*c^2*d^4 + d^6)*f)*log(1/4*(8*a^3*c + sqrt(-64*I*a^6/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*((I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) - sqrt(-64*I*a^6/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*((3*c^4*d^2 - 12*I*c^3*d^3 - 18*c^2*d^4 + 12*I*c*d^5 + 3*d^6)*f*e^(4*I*f*x + 4*I*e) + (6*c^4*d^2 - 12*I*c^3*d^3 - 12*I*c*d^5 - 6*d^6)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4*d^2 + 2*c^2*d^4 + d^6)*f)*log(1/4*(8*a^3*c + sqrt(-64*I*a^6/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (8*a^3*c - 8*I*a^3*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^3) + (16*I*a^3*c^3 + 32*a^3*c^2*d + 112*I*a^3*c*d^2 - 64*a^3*d^3 + (16*I*a^3*c^3 + 80*a^3*c^2*d + 16*I*a^3*c*d^2 + 80*a^3*d^3)*e^(4*I*f*x + 4*I*e) + (32*I*a^3*c^3 + 112*a^3*c^2*d + 128*I*a^3*c*d^2 + 16*a^3*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((12*c^4*d^2 - 48*I*c^3*d^3 - 72*c^2*d^4 + 48*I*c*d^5 + 12*d^6)*f*e^(4*I*f*x + 4*I*e) + (24*c^4*d^2 - 48*I*c^3*d^3 - 48*I*c*d^5 - 24*d^6)*f*e^(2*I*f*x + 2*I*e) + 12*(c^4*d^2 + 2*c^2*d^4 + d^6)*f)","B",0
1132,1,919,0,0.641444," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, c^{4} d - 12 i \, c^{3} d^{2} - 18 \, c^{2} d^{3} + 12 i \, c d^{4} + 3 \, d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} d - 12 i \, c^{3} d^{2} - 12 i \, c d^{4} - 6 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} f\right)} \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c + {\left({\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f\right)} \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) - {\left({\left(3 \, c^{4} d - 12 i \, c^{3} d^{2} - 18 \, c^{2} d^{3} + 12 i \, c d^{4} + 3 \, d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} d - 12 i \, c^{3} d^{2} - 12 i \, c d^{4} - 6 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} f\right)} \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left(4 \, a^{2} c + {\left({\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f\right)} \sqrt{-\frac{16 i \, a^{4}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(4 \, a^{2} c - 4 i \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a^{2}}\right) + 8 \, {\left(a^{2} c^{2} + 6 i \, a^{2} c d - 5 \, a^{2} d^{2} + {\left(a^{2} c^{2} + 6 i \, a^{2} c d + 7 \, a^{2} d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(a^{2} c^{2} + 6 i \, a^{2} c d + a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(12 \, c^{4} d - 48 i \, c^{3} d^{2} - 72 \, c^{2} d^{3} + 48 i \, c d^{4} + 12 \, d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 \, c^{4} d - 48 i \, c^{3} d^{2} - 48 i \, c d^{4} - 24 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 12 \, {\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} f}"," ",0,"(((3*c^4*d - 12*I*c^3*d^2 - 18*c^2*d^3 + 12*I*c*d^4 + 3*d^5)*f*e^(4*I*f*x + 4*I*e) + (6*c^4*d - 12*I*c^3*d^2 - 12*I*c*d^4 - 6*d^5)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4*d + 2*c^2*d^3 + d^5)*f)*sqrt(-16*I*a^4/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(1/2*(4*a^2*c + ((I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f)*sqrt(-16*I*a^4/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) - ((3*c^4*d - 12*I*c^3*d^2 - 18*c^2*d^3 + 12*I*c*d^4 + 3*d^5)*f*e^(4*I*f*x + 4*I*e) + (6*c^4*d - 12*I*c^3*d^2 - 12*I*c*d^4 - 6*d^5)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4*d + 2*c^2*d^3 + d^5)*f)*sqrt(-16*I*a^4/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(1/2*(4*a^2*c + ((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f)*sqrt(-16*I*a^4/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + (4*a^2*c - 4*I*a^2*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a^2) + 8*(a^2*c^2 + 6*I*a^2*c*d - 5*a^2*d^2 + (a^2*c^2 + 6*I*a^2*c*d + 7*a^2*d^2)*e^(4*I*f*x + 4*I*e) + 2*(a^2*c^2 + 6*I*a^2*c*d + a^2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((12*c^4*d - 48*I*c^3*d^2 - 72*c^2*d^3 + 48*I*c*d^4 + 12*d^5)*f*e^(4*I*f*x + 4*I*e) + (24*c^4*d - 48*I*c^3*d^2 - 48*I*c*d^4 - 24*d^5)*f*e^(2*I*f*x + 2*I*e) + 12*(c^4*d + 2*c^2*d^3 + d^5)*f)","B",0
1133,1,839,0,0.634739," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, c^{4} - 12 i \, c^{3} d - 18 \, c^{2} d^{2} + 12 i \, c d^{3} + 3 \, d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} - 12 i \, c^{3} d - 12 i \, c d^{3} - 6 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f\right)} \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left({\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - {\left({\left(3 \, c^{4} - 12 i \, c^{3} d - 18 \, c^{2} d^{2} + 12 i \, c d^{3} + 3 \, d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} - 12 i \, c^{3} d - 12 i \, c d^{3} - 6 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f\right)} \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left(2 \, a c + {\left({\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{4 i \, a^{2}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} + {\left(2 \, a c - 2 i \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{a}\right) - 16 \, {\left(-2 i \, a c + a d + 2 \, {\left(-i \, a c - a d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-4 i \, a c - a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(12 \, c^{4} - 48 i \, c^{3} d - 72 \, c^{2} d^{2} + 48 i \, c d^{3} + 12 \, d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(24 \, c^{4} - 48 i \, c^{3} d - 48 i \, c d^{3} - 24 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 12 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f}"," ",0,"(((3*c^4 - 12*I*c^3*d - 18*c^2*d^2 + 12*I*c*d^3 + 3*d^4)*f*e^(4*I*f*x + 4*I*e) + (6*c^4 - 12*I*c^3*d - 12*I*c*d^3 - 6*d^4)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4 + 2*c^2*d^2 + d^4)*f)*sqrt(-4*I*a^2/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log((2*a*c + ((I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2)) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) - ((3*c^4 - 12*I*c^3*d - 18*c^2*d^2 + 12*I*c*d^3 + 3*d^4)*f*e^(4*I*f*x + 4*I*e) + (6*c^4 - 12*I*c^3*d - 12*I*c*d^3 - 6*d^4)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4 + 2*c^2*d^2 + d^4)*f)*sqrt(-4*I*a^2/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log((2*a*c + ((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-4*I*a^2/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2)) + (2*a*c - 2*I*a*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/a) - 16*(-2*I*a*c + a*d + 2*(-I*a*c - a*d)*e^(4*I*f*x + 4*I*e) + (-4*I*a*c - a*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((12*c^4 - 48*I*c^3*d - 72*c^2*d^2 + 48*I*c*d^3 + 12*d^4)*f*e^(4*I*f*x + 4*I*e) + (24*c^4 - 48*I*c^3*d - 48*I*c*d^3 - 24*d^4)*f*e^(2*I*f*x + 2*I*e) + 12*(c^4 + 2*c^2*d^2 + d^4)*f)","B",0
1134,1,2668,0,3.197913," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 i \, a c^{7} + 3 \, a c^{6} d + 9 i \, a c^{5} d^{2} + 9 \, a c^{4} d^{3} + 9 i \, a c^{3} d^{4} + 9 \, a c^{2} d^{5} + 3 i \, a c d^{6} + 3 \, a d^{7}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(6 i \, a c^{7} - 6 \, a c^{6} d + 18 i \, a c^{5} d^{2} - 18 \, a c^{4} d^{3} + 18 i \, a c^{3} d^{4} - 18 \, a c^{2} d^{5} + 6 i \, a c d^{6} - 6 \, a d^{7}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3 i \, a c^{7} - 9 \, a c^{6} d - 3 i \, a c^{5} d^{2} - 15 \, a c^{4} d^{3} - 15 i \, a c^{3} d^{4} - 3 \, a c^{2} d^{5} - 9 i \, a c d^{6} + 3 \, a d^{7}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d - 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} + 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} \log\left({\left({\left({\left(4 i \, a c^{3} + 12 \, a c^{2} d - 12 i \, a c d^{2} - 4 \, a d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 i \, a c^{3} + 12 \, a c^{2} d - 12 i \, a c d^{2} - 4 \, a d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{{\left(4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d - 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} + 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(-3 i \, a c^{7} - 3 \, a c^{6} d - 9 i \, a c^{5} d^{2} - 9 \, a c^{4} d^{3} - 9 i \, a c^{3} d^{4} - 9 \, a c^{2} d^{5} - 3 i \, a c d^{6} - 3 \, a d^{7}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-6 i \, a c^{7} + 6 \, a c^{6} d - 18 i \, a c^{5} d^{2} + 18 \, a c^{4} d^{3} - 18 i \, a c^{3} d^{4} + 18 \, a c^{2} d^{5} - 6 i \, a c d^{6} + 6 \, a d^{7}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-3 i \, a c^{7} + 9 \, a c^{6} d + 3 i \, a c^{5} d^{2} + 15 \, a c^{4} d^{3} + 15 i \, a c^{3} d^{4} + 3 \, a c^{2} d^{5} + 9 i \, a c d^{6} - 3 \, a d^{7}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d - 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} + 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} \log\left({\left({\left({\left(-4 i \, a c^{3} - 12 \, a c^{2} d + 12 i \, a c d^{2} + 4 \, a d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-4 i \, a c^{3} - 12 \, a c^{2} d + 12 i \, a c d^{2} + 4 \, a d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{{\left(4 i \, a^{2} c^{5} + 20 \, a^{2} c^{4} d - 40 i \, a^{2} c^{3} d^{2} - 40 \, a^{2} c^{2} d^{3} + 20 i \, a^{2} c d^{4} + 4 \, a^{2} d^{5}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(3 i \, a c^{7} + 3 \, a c^{6} d + 9 i \, a c^{5} d^{2} + 9 \, a c^{4} d^{3} + 9 i \, a c^{3} d^{4} + 9 \, a c^{2} d^{5} + 3 i \, a c d^{6} + 3 \, a d^{7}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(6 i \, a c^{7} - 6 \, a c^{6} d + 18 i \, a c^{5} d^{2} - 18 \, a c^{4} d^{3} + 18 i \, a c^{3} d^{4} - 18 \, a c^{2} d^{5} + 6 i \, a c d^{6} - 6 \, a d^{7}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3 i \, a c^{7} - 9 \, a c^{6} d - 3 i \, a c^{5} d^{2} - 15 \, a c^{4} d^{3} - 15 i \, a c^{3} d^{4} - 3 \, a c^{2} d^{5} - 9 i \, a c d^{6} + 3 \, a d^{7}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{-i \, c^{2} + 12 \, c d + 36 i \, d^{2}}{{\left(4 i \, a^{2} c^{7} - 28 \, a^{2} c^{6} d - 84 i \, a^{2} c^{5} d^{2} + 140 \, a^{2} c^{4} d^{3} + 140 i \, a^{2} c^{3} d^{4} - 84 \, a^{2} c^{2} d^{5} - 28 i \, a^{2} c d^{6} + 4 \, a^{2} d^{7}\right)} f^{2}}} \log\left(\frac{{\left(i \, c^{2} - 7 \, c d - 6 i \, d^{2} + {\left({\left(2 \, a c^{4} + 8 i \, a c^{3} d - 12 \, a c^{2} d^{2} - 8 i \, a c d^{3} + 2 \, a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 \, a c^{4} + 8 i \, a c^{3} d - 12 \, a c^{2} d^{2} - 8 i \, a c d^{3} + 2 \, a d^{4}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-i \, c^{2} + 12 \, c d + 36 i \, d^{2}}{{\left(4 i \, a^{2} c^{7} - 28 \, a^{2} c^{6} d - 84 i \, a^{2} c^{5} d^{2} + 140 \, a^{2} c^{4} d^{3} + 140 i \, a^{2} c^{3} d^{4} - 84 \, a^{2} c^{2} d^{5} - 28 i \, a^{2} c d^{6} + 4 \, a^{2} d^{7}\right)} f^{2}}} + {\left(i \, c^{2} - 6 \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(2 \, a c^{4} + 8 i \, a c^{3} d - 12 \, a c^{2} d^{2} - 8 i \, a c d^{3} + 2 \, a d^{4}\right)} f}\right) + {\left({\left(-3 i \, a c^{7} - 3 \, a c^{6} d - 9 i \, a c^{5} d^{2} - 9 \, a c^{4} d^{3} - 9 i \, a c^{3} d^{4} - 9 \, a c^{2} d^{5} - 3 i \, a c d^{6} - 3 \, a d^{7}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-6 i \, a c^{7} + 6 \, a c^{6} d - 18 i \, a c^{5} d^{2} + 18 \, a c^{4} d^{3} - 18 i \, a c^{3} d^{4} + 18 \, a c^{2} d^{5} - 6 i \, a c d^{6} + 6 \, a d^{7}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-3 i \, a c^{7} + 9 \, a c^{6} d + 3 i \, a c^{5} d^{2} + 15 \, a c^{4} d^{3} + 15 i \, a c^{3} d^{4} + 3 \, a c^{2} d^{5} + 9 i \, a c d^{6} - 3 \, a d^{7}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{-i \, c^{2} + 12 \, c d + 36 i \, d^{2}}{{\left(4 i \, a^{2} c^{7} - 28 \, a^{2} c^{6} d - 84 i \, a^{2} c^{5} d^{2} + 140 \, a^{2} c^{4} d^{3} + 140 i \, a^{2} c^{3} d^{4} - 84 \, a^{2} c^{2} d^{5} - 28 i \, a^{2} c d^{6} + 4 \, a^{2} d^{7}\right)} f^{2}}} \log\left(\frac{{\left(i \, c^{2} - 7 \, c d - 6 i \, d^{2} - {\left({\left(2 \, a c^{4} + 8 i \, a c^{3} d - 12 \, a c^{2} d^{2} - 8 i \, a c d^{3} + 2 \, a d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 \, a c^{4} + 8 i \, a c^{3} d - 12 \, a c^{2} d^{2} - 8 i \, a c d^{3} + 2 \, a d^{4}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-i \, c^{2} + 12 \, c d + 36 i \, d^{2}}{{\left(4 i \, a^{2} c^{7} - 28 \, a^{2} c^{6} d - 84 i \, a^{2} c^{5} d^{2} + 140 \, a^{2} c^{4} d^{3} + 140 i \, a^{2} c^{3} d^{4} - 84 \, a^{2} c^{2} d^{5} - 28 i \, a^{2} c d^{6} + 4 \, a^{2} d^{7}\right)} f^{2}}} + {\left(i \, c^{2} - 6 \, c d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(2 \, a c^{4} + 8 i \, a c^{3} d - 12 \, a c^{2} d^{2} - 8 i \, a c d^{3} + 2 \, a d^{4}\right)} f}\right) - {\left(3 \, c^{4} + 6 \, c^{2} d^{2} + 3 \, d^{4} + {\left(3 \, c^{4} - 12 i \, c^{3} d - 98 \, c^{2} d^{2} + 108 i \, c d^{3} + 19 \, d^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(9 \, c^{4} - 24 i \, c^{3} d - 178 \, c^{2} d^{2} + 48 i \, c d^{3} - 19 \, d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(9 \, c^{4} - 12 i \, c^{3} d - 74 \, c^{2} d^{2} - 60 i \, c d^{3} - 35 \, d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(12 i \, a c^{7} + 12 \, a c^{6} d + 36 i \, a c^{5} d^{2} + 36 \, a c^{4} d^{3} + 36 i \, a c^{3} d^{4} + 36 \, a c^{2} d^{5} + 12 i \, a c d^{6} + 12 \, a d^{7}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(24 i \, a c^{7} - 24 \, a c^{6} d + 72 i \, a c^{5} d^{2} - 72 \, a c^{4} d^{3} + 72 i \, a c^{3} d^{4} - 72 \, a c^{2} d^{5} + 24 i \, a c d^{6} - 24 \, a d^{7}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(12 i \, a c^{7} - 36 \, a c^{6} d - 12 i \, a c^{5} d^{2} - 60 \, a c^{4} d^{3} - 60 i \, a c^{3} d^{4} - 12 \, a c^{2} d^{5} - 36 i \, a c d^{6} + 12 \, a d^{7}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)}}"," ",0,"(((3*I*a*c^7 + 3*a*c^6*d + 9*I*a*c^5*d^2 + 9*a*c^4*d^3 + 9*I*a*c^3*d^4 + 9*a*c^2*d^5 + 3*I*a*c*d^6 + 3*a*d^7)*f*e^(6*I*f*x + 6*I*e) + (6*I*a*c^7 - 6*a*c^6*d + 18*I*a*c^5*d^2 - 18*a*c^4*d^3 + 18*I*a*c^3*d^4 - 18*a*c^2*d^5 + 6*I*a*c*d^6 - 6*a*d^7)*f*e^(4*I*f*x + 4*I*e) + (3*I*a*c^7 - 9*a*c^6*d - 3*I*a*c^5*d^2 - 15*a*c^4*d^3 - 15*I*a*c^3*d^4 - 3*a*c^2*d^5 - 9*I*a*c*d^6 + 3*a*d^7)*f*e^(2*I*f*x + 2*I*e))*sqrt(-I/((4*I*a^2*c^5 + 20*a^2*c^4*d - 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 + 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2))*log((((4*I*a*c^3 + 12*a*c^2*d - 12*I*a*c*d^2 - 4*a*d^3)*f*e^(2*I*f*x + 2*I*e) + (4*I*a*c^3 + 12*a*c^2*d - 12*I*a*c*d^2 - 4*a*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-I/((4*I*a^2*c^5 + 20*a^2*c^4*d - 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 + 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((-3*I*a*c^7 - 3*a*c^6*d - 9*I*a*c^5*d^2 - 9*a*c^4*d^3 - 9*I*a*c^3*d^4 - 9*a*c^2*d^5 - 3*I*a*c*d^6 - 3*a*d^7)*f*e^(6*I*f*x + 6*I*e) + (-6*I*a*c^7 + 6*a*c^6*d - 18*I*a*c^5*d^2 + 18*a*c^4*d^3 - 18*I*a*c^3*d^4 + 18*a*c^2*d^5 - 6*I*a*c*d^6 + 6*a*d^7)*f*e^(4*I*f*x + 4*I*e) + (-3*I*a*c^7 + 9*a*c^6*d + 3*I*a*c^5*d^2 + 15*a*c^4*d^3 + 15*I*a*c^3*d^4 + 3*a*c^2*d^5 + 9*I*a*c*d^6 - 3*a*d^7)*f*e^(2*I*f*x + 2*I*e))*sqrt(-I/((4*I*a^2*c^5 + 20*a^2*c^4*d - 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 + 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2))*log((((-4*I*a*c^3 - 12*a*c^2*d + 12*I*a*c*d^2 + 4*a*d^3)*f*e^(2*I*f*x + 2*I*e) + (-4*I*a*c^3 - 12*a*c^2*d + 12*I*a*c*d^2 + 4*a*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-I/((4*I*a^2*c^5 + 20*a^2*c^4*d - 40*I*a^2*c^3*d^2 - 40*a^2*c^2*d^3 + 20*I*a^2*c*d^4 + 4*a^2*d^5)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((3*I*a*c^7 + 3*a*c^6*d + 9*I*a*c^5*d^2 + 9*a*c^4*d^3 + 9*I*a*c^3*d^4 + 9*a*c^2*d^5 + 3*I*a*c*d^6 + 3*a*d^7)*f*e^(6*I*f*x + 6*I*e) + (6*I*a*c^7 - 6*a*c^6*d + 18*I*a*c^5*d^2 - 18*a*c^4*d^3 + 18*I*a*c^3*d^4 - 18*a*c^2*d^5 + 6*I*a*c*d^6 - 6*a*d^7)*f*e^(4*I*f*x + 4*I*e) + (3*I*a*c^7 - 9*a*c^6*d - 3*I*a*c^5*d^2 - 15*a*c^4*d^3 - 15*I*a*c^3*d^4 - 3*a*c^2*d^5 - 9*I*a*c*d^6 + 3*a*d^7)*f*e^(2*I*f*x + 2*I*e))*sqrt((-I*c^2 + 12*c*d + 36*I*d^2)/((4*I*a^2*c^7 - 28*a^2*c^6*d - 84*I*a^2*c^5*d^2 + 140*a^2*c^4*d^3 + 140*I*a^2*c^3*d^4 - 84*a^2*c^2*d^5 - 28*I*a^2*c*d^6 + 4*a^2*d^7)*f^2))*log((I*c^2 - 7*c*d - 6*I*d^2 + ((2*a*c^4 + 8*I*a*c^3*d - 12*a*c^2*d^2 - 8*I*a*c*d^3 + 2*a*d^4)*f*e^(2*I*f*x + 2*I*e) + (2*a*c^4 + 8*I*a*c^3*d - 12*a*c^2*d^2 - 8*I*a*c*d^3 + 2*a*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-I*c^2 + 12*c*d + 36*I*d^2)/((4*I*a^2*c^7 - 28*a^2*c^6*d - 84*I*a^2*c^5*d^2 + 140*a^2*c^4*d^3 + 140*I*a^2*c^3*d^4 - 84*a^2*c^2*d^5 - 28*I*a^2*c*d^6 + 4*a^2*d^7)*f^2)) + (I*c^2 - 6*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((2*a*c^4 + 8*I*a*c^3*d - 12*a*c^2*d^2 - 8*I*a*c*d^3 + 2*a*d^4)*f)) + ((-3*I*a*c^7 - 3*a*c^6*d - 9*I*a*c^5*d^2 - 9*a*c^4*d^3 - 9*I*a*c^3*d^4 - 9*a*c^2*d^5 - 3*I*a*c*d^6 - 3*a*d^7)*f*e^(6*I*f*x + 6*I*e) + (-6*I*a*c^7 + 6*a*c^6*d - 18*I*a*c^5*d^2 + 18*a*c^4*d^3 - 18*I*a*c^3*d^4 + 18*a*c^2*d^5 - 6*I*a*c*d^6 + 6*a*d^7)*f*e^(4*I*f*x + 4*I*e) + (-3*I*a*c^7 + 9*a*c^6*d + 3*I*a*c^5*d^2 + 15*a*c^4*d^3 + 15*I*a*c^3*d^4 + 3*a*c^2*d^5 + 9*I*a*c*d^6 - 3*a*d^7)*f*e^(2*I*f*x + 2*I*e))*sqrt((-I*c^2 + 12*c*d + 36*I*d^2)/((4*I*a^2*c^7 - 28*a^2*c^6*d - 84*I*a^2*c^5*d^2 + 140*a^2*c^4*d^3 + 140*I*a^2*c^3*d^4 - 84*a^2*c^2*d^5 - 28*I*a^2*c*d^6 + 4*a^2*d^7)*f^2))*log((I*c^2 - 7*c*d - 6*I*d^2 - ((2*a*c^4 + 8*I*a*c^3*d - 12*a*c^2*d^2 - 8*I*a*c*d^3 + 2*a*d^4)*f*e^(2*I*f*x + 2*I*e) + (2*a*c^4 + 8*I*a*c^3*d - 12*a*c^2*d^2 - 8*I*a*c*d^3 + 2*a*d^4)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-I*c^2 + 12*c*d + 36*I*d^2)/((4*I*a^2*c^7 - 28*a^2*c^6*d - 84*I*a^2*c^5*d^2 + 140*a^2*c^4*d^3 + 140*I*a^2*c^3*d^4 - 84*a^2*c^2*d^5 - 28*I*a^2*c*d^6 + 4*a^2*d^7)*f^2)) + (I*c^2 - 6*c*d)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((2*a*c^4 + 8*I*a*c^3*d - 12*a*c^2*d^2 - 8*I*a*c*d^3 + 2*a*d^4)*f)) - (3*c^4 + 6*c^2*d^2 + 3*d^4 + (3*c^4 - 12*I*c^3*d - 98*c^2*d^2 + 108*I*c*d^3 + 19*d^4)*e^(6*I*f*x + 6*I*e) + (9*c^4 - 24*I*c^3*d - 178*c^2*d^2 + 48*I*c*d^3 - 19*d^4)*e^(4*I*f*x + 4*I*e) + (9*c^4 - 12*I*c^3*d - 74*c^2*d^2 - 60*I*c*d^3 - 35*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((12*I*a*c^7 + 12*a*c^6*d + 36*I*a*c^5*d^2 + 36*a*c^4*d^3 + 36*I*a*c^3*d^4 + 36*a*c^2*d^5 + 12*I*a*c*d^6 + 12*a*d^7)*f*e^(6*I*f*x + 6*I*e) + (24*I*a*c^7 - 24*a*c^6*d + 72*I*a*c^5*d^2 - 72*a*c^4*d^3 + 72*I*a*c^3*d^4 - 72*a*c^2*d^5 + 24*I*a*c*d^6 - 24*a*d^7)*f*e^(4*I*f*x + 4*I*e) + (12*I*a*c^7 - 36*a*c^6*d - 12*I*a*c^5*d^2 - 60*a*c^4*d^3 - 60*I*a*c^3*d^4 - 12*a*c^2*d^5 - 36*I*a*c*d^6 + 12*a*d^7)*f*e^(2*I*f*x + 2*I*e))","B",0
1135,1,3248,0,10.196035," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(12 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d + 48 \, a^{2} c^{6} d^{2} + 144 i \, a^{2} c^{5} d^{3} + 144 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} + 48 i \, a^{2} c d^{7} - 24 \, a^{2} d^{8}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(12 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d - 48 \, a^{2} c^{6} d^{2} + 48 i \, a^{2} c^{5} d^{3} - 120 \, a^{2} c^{4} d^{4} - 48 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} - 48 i \, a^{2} c d^{7} + 12 \, a^{2} d^{8}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(16 i \, a^{4} c^{5} + 80 \, a^{4} c^{4} d - 160 i \, a^{4} c^{3} d^{2} - 160 \, a^{4} c^{2} d^{3} + 80 i \, a^{4} c d^{4} + 16 \, a^{4} d^{5}\right)} f^{2}}} \log\left({\left({\left({\left(8 i \, a^{2} c^{3} + 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} - 8 \, a^{2} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, a^{2} c^{3} + 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} - 8 \, a^{2} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{{\left(16 i \, a^{4} c^{5} + 80 \, a^{4} c^{4} d - 160 i \, a^{4} c^{3} d^{2} - 160 \, a^{4} c^{2} d^{3} + 80 i \, a^{4} c d^{4} + 16 \, a^{4} d^{5}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left(12 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d + 48 \, a^{2} c^{6} d^{2} + 144 i \, a^{2} c^{5} d^{3} + 144 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} + 48 i \, a^{2} c d^{7} - 24 \, a^{2} d^{8}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(12 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d - 48 \, a^{2} c^{6} d^{2} + 48 i \, a^{2} c^{5} d^{3} - 120 \, a^{2} c^{4} d^{4} - 48 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} - 48 i \, a^{2} c d^{7} + 12 \, a^{2} d^{8}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(16 i \, a^{4} c^{5} + 80 \, a^{4} c^{4} d - 160 i \, a^{4} c^{3} d^{2} - 160 \, a^{4} c^{2} d^{3} + 80 i \, a^{4} c d^{4} + 16 \, a^{4} d^{5}\right)} f^{2}}} \log\left({\left({\left({\left(-8 i \, a^{2} c^{3} - 24 \, a^{2} c^{2} d + 24 i \, a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, a^{2} c^{3} - 24 \, a^{2} c^{2} d + 24 i \, a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{{\left(16 i \, a^{4} c^{5} + 80 \, a^{4} c^{4} d - 160 i \, a^{4} c^{3} d^{2} - 160 \, a^{4} c^{2} d^{3} + 80 i \, a^{4} c d^{4} + 16 \, a^{4} d^{5}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - {\left(12 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d + 48 \, a^{2} c^{6} d^{2} + 144 i \, a^{2} c^{5} d^{3} + 144 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} + 48 i \, a^{2} c d^{7} - 24 \, a^{2} d^{8}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(12 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d - 48 \, a^{2} c^{6} d^{2} + 48 i \, a^{2} c^{5} d^{3} - 120 \, a^{2} c^{4} d^{4} - 48 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} - 48 i \, a^{2} c d^{7} + 12 \, a^{2} d^{8}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{4 i \, c^{4} - 56 \, c^{3} d - 384 i \, c^{2} d^{2} + 1316 \, c d^{3} + 2209 i \, d^{4}}{{\left(-64 i \, a^{4} c^{9} + 576 \, a^{4} c^{8} d + 2304 i \, a^{4} c^{7} d^{2} - 5376 \, a^{4} c^{6} d^{3} - 8064 i \, a^{4} c^{5} d^{4} + 8064 \, a^{4} c^{4} d^{5} + 5376 i \, a^{4} c^{3} d^{6} - 2304 \, a^{4} c^{2} d^{7} - 576 i \, a^{4} c d^{8} + 64 \, a^{4} d^{9}\right)} f^{2}}} \log\left(\frac{{\left(2 \, c^{3} + 16 i \, c^{2} d - 61 \, c d^{2} - 47 i \, d^{3} + {\left({\left(8 i \, a^{2} c^{5} - 40 \, a^{2} c^{4} d - 80 i \, a^{2} c^{3} d^{2} + 80 \, a^{2} c^{2} d^{3} + 40 i \, a^{2} c d^{4} - 8 \, a^{2} d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(8 i \, a^{2} c^{5} - 40 \, a^{2} c^{4} d - 80 i \, a^{2} c^{3} d^{2} + 80 \, a^{2} c^{2} d^{3} + 40 i \, a^{2} c d^{4} - 8 \, a^{2} d^{5}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{4} - 56 \, c^{3} d - 384 i \, c^{2} d^{2} + 1316 \, c d^{3} + 2209 i \, d^{4}}{{\left(-64 i \, a^{4} c^{9} + 576 \, a^{4} c^{8} d + 2304 i \, a^{4} c^{7} d^{2} - 5376 \, a^{4} c^{6} d^{3} - 8064 i \, a^{4} c^{5} d^{4} + 8064 \, a^{4} c^{4} d^{5} + 5376 i \, a^{4} c^{3} d^{6} - 2304 \, a^{4} c^{2} d^{7} - 576 i \, a^{4} c d^{8} + 64 \, a^{4} d^{9}\right)} f^{2}}} + {\left(2 \, c^{3} + 14 i \, c^{2} d - 47 \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(-8 i \, a^{2} c^{5} + 40 \, a^{2} c^{4} d + 80 i \, a^{2} c^{3} d^{2} - 80 \, a^{2} c^{2} d^{3} - 40 i \, a^{2} c d^{4} + 8 \, a^{2} d^{5}\right)} f}\right) + {\left(12 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d + 48 \, a^{2} c^{6} d^{2} + 144 i \, a^{2} c^{5} d^{3} + 144 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} + 48 i \, a^{2} c d^{7} - 24 \, a^{2} d^{8}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(12 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d - 48 \, a^{2} c^{6} d^{2} + 48 i \, a^{2} c^{5} d^{3} - 120 \, a^{2} c^{4} d^{4} - 48 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} - 48 i \, a^{2} c d^{7} + 12 \, a^{2} d^{8}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}\right)} \sqrt{\frac{4 i \, c^{4} - 56 \, c^{3} d - 384 i \, c^{2} d^{2} + 1316 \, c d^{3} + 2209 i \, d^{4}}{{\left(-64 i \, a^{4} c^{9} + 576 \, a^{4} c^{8} d + 2304 i \, a^{4} c^{7} d^{2} - 5376 \, a^{4} c^{6} d^{3} - 8064 i \, a^{4} c^{5} d^{4} + 8064 \, a^{4} c^{4} d^{5} + 5376 i \, a^{4} c^{3} d^{6} - 2304 \, a^{4} c^{2} d^{7} - 576 i \, a^{4} c d^{8} + 64 \, a^{4} d^{9}\right)} f^{2}}} \log\left(\frac{{\left(2 \, c^{3} + 16 i \, c^{2} d - 61 \, c d^{2} - 47 i \, d^{3} + {\left({\left(-8 i \, a^{2} c^{5} + 40 \, a^{2} c^{4} d + 80 i \, a^{2} c^{3} d^{2} - 80 \, a^{2} c^{2} d^{3} - 40 i \, a^{2} c d^{4} + 8 \, a^{2} d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-8 i \, a^{2} c^{5} + 40 \, a^{2} c^{4} d + 80 i \, a^{2} c^{3} d^{2} - 80 \, a^{2} c^{2} d^{3} - 40 i \, a^{2} c d^{4} + 8 \, a^{2} d^{5}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{4 i \, c^{4} - 56 \, c^{3} d - 384 i \, c^{2} d^{2} + 1316 \, c d^{3} + 2209 i \, d^{4}}{{\left(-64 i \, a^{4} c^{9} + 576 \, a^{4} c^{8} d + 2304 i \, a^{4} c^{7} d^{2} - 5376 \, a^{4} c^{6} d^{3} - 8064 i \, a^{4} c^{5} d^{4} + 8064 \, a^{4} c^{4} d^{5} + 5376 i \, a^{4} c^{3} d^{6} - 2304 \, a^{4} c^{2} d^{7} - 576 i \, a^{4} c d^{8} + 64 \, a^{4} d^{9}\right)} f^{2}}} + {\left(2 \, c^{3} + 14 i \, c^{2} d - 47 \, c d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(-8 i \, a^{2} c^{5} + 40 \, a^{2} c^{4} d + 80 i \, a^{2} c^{3} d^{2} - 80 \, a^{2} c^{2} d^{3} - 40 i \, a^{2} c d^{4} + 8 \, a^{2} d^{5}\right)} f}\right) + {\left(3 i \, c^{5} - 3 \, c^{4} d + 6 i \, c^{3} d^{2} - 6 \, c^{2} d^{3} + 3 i \, c d^{4} - 3 \, d^{5} + {\left(9 i \, c^{5} - 6 \, c^{4} d + 114 i \, c^{3} d^{2} + 632 \, c^{2} d^{3} - 735 i \, c d^{4} - 202 \, d^{5}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(30 i \, c^{5} - 45 \, c^{4} d + 276 i \, c^{3} d^{2} + 1090 \, c^{2} d^{3} - 402 i \, c d^{4} + 103 \, d^{5}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(36 i \, c^{5} - 75 \, c^{4} d + 192 i \, c^{3} d^{2} + 386 \, c^{2} d^{3} + 348 i \, c d^{4} + 269 \, d^{5}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(18 i \, c^{5} - 39 \, c^{4} d + 36 i \, c^{3} d^{2} - 78 \, c^{2} d^{3} + 18 i \, c d^{4} - 39 \, d^{5}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{48 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(96 \, a^{2} c^{8} + 192 i \, a^{2} c^{7} d + 192 \, a^{2} c^{6} d^{2} + 576 i \, a^{2} c^{5} d^{3} + 576 i \, a^{2} c^{3} d^{5} - 192 \, a^{2} c^{2} d^{6} + 192 i \, a^{2} c d^{7} - 96 \, a^{2} d^{8}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(48 \, a^{2} c^{8} + 192 i \, a^{2} c^{7} d - 192 \, a^{2} c^{6} d^{2} + 192 i \, a^{2} c^{5} d^{3} - 480 \, a^{2} c^{4} d^{4} - 192 i \, a^{2} c^{3} d^{5} - 192 \, a^{2} c^{2} d^{6} - 192 i \, a^{2} c d^{7} + 48 \, a^{2} d^{8}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)}}"," ",0,"((12*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(8*I*f*x + 8*I*e) + (24*a^2*c^8 + 48*I*a^2*c^7*d + 48*a^2*c^6*d^2 + 144*I*a^2*c^5*d^3 + 144*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 + 48*I*a^2*c*d^7 - 24*a^2*d^8)*f*e^(6*I*f*x + 6*I*e) + (12*a^2*c^8 + 48*I*a^2*c^7*d - 48*a^2*c^6*d^2 + 48*I*a^2*c^5*d^3 - 120*a^2*c^4*d^4 - 48*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 - 48*I*a^2*c*d^7 + 12*a^2*d^8)*f*e^(4*I*f*x + 4*I*e))*sqrt(-I/((16*I*a^4*c^5 + 80*a^4*c^4*d - 160*I*a^4*c^3*d^2 - 160*a^4*c^2*d^3 + 80*I*a^4*c*d^4 + 16*a^4*d^5)*f^2))*log((((8*I*a^2*c^3 + 24*a^2*c^2*d - 24*I*a^2*c*d^2 - 8*a^2*d^3)*f*e^(2*I*f*x + 2*I*e) + (8*I*a^2*c^3 + 24*a^2*c^2*d - 24*I*a^2*c*d^2 - 8*a^2*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-I/((16*I*a^4*c^5 + 80*a^4*c^4*d - 160*I*a^4*c^3*d^2 - 160*a^4*c^2*d^3 + 80*I*a^4*c*d^4 + 16*a^4*d^5)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) - (12*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(8*I*f*x + 8*I*e) + (24*a^2*c^8 + 48*I*a^2*c^7*d + 48*a^2*c^6*d^2 + 144*I*a^2*c^5*d^3 + 144*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 + 48*I*a^2*c*d^7 - 24*a^2*d^8)*f*e^(6*I*f*x + 6*I*e) + (12*a^2*c^8 + 48*I*a^2*c^7*d - 48*a^2*c^6*d^2 + 48*I*a^2*c^5*d^3 - 120*a^2*c^4*d^4 - 48*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 - 48*I*a^2*c*d^7 + 12*a^2*d^8)*f*e^(4*I*f*x + 4*I*e))*sqrt(-I/((16*I*a^4*c^5 + 80*a^4*c^4*d - 160*I*a^4*c^3*d^2 - 160*a^4*c^2*d^3 + 80*I*a^4*c*d^4 + 16*a^4*d^5)*f^2))*log((((-8*I*a^2*c^3 - 24*a^2*c^2*d + 24*I*a^2*c*d^2 + 8*a^2*d^3)*f*e^(2*I*f*x + 2*I*e) + (-8*I*a^2*c^3 - 24*a^2*c^2*d + 24*I*a^2*c*d^2 + 8*a^2*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-I/((16*I*a^4*c^5 + 80*a^4*c^4*d - 160*I*a^4*c^3*d^2 - 160*a^4*c^2*d^3 + 80*I*a^4*c*d^4 + 16*a^4*d^5)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) - (12*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(8*I*f*x + 8*I*e) + (24*a^2*c^8 + 48*I*a^2*c^7*d + 48*a^2*c^6*d^2 + 144*I*a^2*c^5*d^3 + 144*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 + 48*I*a^2*c*d^7 - 24*a^2*d^8)*f*e^(6*I*f*x + 6*I*e) + (12*a^2*c^8 + 48*I*a^2*c^7*d - 48*a^2*c^6*d^2 + 48*I*a^2*c^5*d^3 - 120*a^2*c^4*d^4 - 48*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 - 48*I*a^2*c*d^7 + 12*a^2*d^8)*f*e^(4*I*f*x + 4*I*e))*sqrt((4*I*c^4 - 56*c^3*d - 384*I*c^2*d^2 + 1316*c*d^3 + 2209*I*d^4)/((-64*I*a^4*c^9 + 576*a^4*c^8*d + 2304*I*a^4*c^7*d^2 - 5376*a^4*c^6*d^3 - 8064*I*a^4*c^5*d^4 + 8064*a^4*c^4*d^5 + 5376*I*a^4*c^3*d^6 - 2304*a^4*c^2*d^7 - 576*I*a^4*c*d^8 + 64*a^4*d^9)*f^2))*log((2*c^3 + 16*I*c^2*d - 61*c*d^2 - 47*I*d^3 + ((8*I*a^2*c^5 - 40*a^2*c^4*d - 80*I*a^2*c^3*d^2 + 80*a^2*c^2*d^3 + 40*I*a^2*c*d^4 - 8*a^2*d^5)*f*e^(2*I*f*x + 2*I*e) + (8*I*a^2*c^5 - 40*a^2*c^4*d - 80*I*a^2*c^3*d^2 + 80*a^2*c^2*d^3 + 40*I*a^2*c*d^4 - 8*a^2*d^5)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^4 - 56*c^3*d - 384*I*c^2*d^2 + 1316*c*d^3 + 2209*I*d^4)/((-64*I*a^4*c^9 + 576*a^4*c^8*d + 2304*I*a^4*c^7*d^2 - 5376*a^4*c^6*d^3 - 8064*I*a^4*c^5*d^4 + 8064*a^4*c^4*d^5 + 5376*I*a^4*c^3*d^6 - 2304*a^4*c^2*d^7 - 576*I*a^4*c*d^8 + 64*a^4*d^9)*f^2)) + (2*c^3 + 14*I*c^2*d - 47*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((-8*I*a^2*c^5 + 40*a^2*c^4*d + 80*I*a^2*c^3*d^2 - 80*a^2*c^2*d^3 - 40*I*a^2*c*d^4 + 8*a^2*d^5)*f)) + (12*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(8*I*f*x + 8*I*e) + (24*a^2*c^8 + 48*I*a^2*c^7*d + 48*a^2*c^6*d^2 + 144*I*a^2*c^5*d^3 + 144*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 + 48*I*a^2*c*d^7 - 24*a^2*d^8)*f*e^(6*I*f*x + 6*I*e) + (12*a^2*c^8 + 48*I*a^2*c^7*d - 48*a^2*c^6*d^2 + 48*I*a^2*c^5*d^3 - 120*a^2*c^4*d^4 - 48*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 - 48*I*a^2*c*d^7 + 12*a^2*d^8)*f*e^(4*I*f*x + 4*I*e))*sqrt((4*I*c^4 - 56*c^3*d - 384*I*c^2*d^2 + 1316*c*d^3 + 2209*I*d^4)/((-64*I*a^4*c^9 + 576*a^4*c^8*d + 2304*I*a^4*c^7*d^2 - 5376*a^4*c^6*d^3 - 8064*I*a^4*c^5*d^4 + 8064*a^4*c^4*d^5 + 5376*I*a^4*c^3*d^6 - 2304*a^4*c^2*d^7 - 576*I*a^4*c*d^8 + 64*a^4*d^9)*f^2))*log((2*c^3 + 16*I*c^2*d - 61*c*d^2 - 47*I*d^3 + ((-8*I*a^2*c^5 + 40*a^2*c^4*d + 80*I*a^2*c^3*d^2 - 80*a^2*c^2*d^3 - 40*I*a^2*c*d^4 + 8*a^2*d^5)*f*e^(2*I*f*x + 2*I*e) + (-8*I*a^2*c^5 + 40*a^2*c^4*d + 80*I*a^2*c^3*d^2 - 80*a^2*c^2*d^3 - 40*I*a^2*c*d^4 + 8*a^2*d^5)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((4*I*c^4 - 56*c^3*d - 384*I*c^2*d^2 + 1316*c*d^3 + 2209*I*d^4)/((-64*I*a^4*c^9 + 576*a^4*c^8*d + 2304*I*a^4*c^7*d^2 - 5376*a^4*c^6*d^3 - 8064*I*a^4*c^5*d^4 + 8064*a^4*c^4*d^5 + 5376*I*a^4*c^3*d^6 - 2304*a^4*c^2*d^7 - 576*I*a^4*c*d^8 + 64*a^4*d^9)*f^2)) + (2*c^3 + 14*I*c^2*d - 47*c*d^2)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((-8*I*a^2*c^5 + 40*a^2*c^4*d + 80*I*a^2*c^3*d^2 - 80*a^2*c^2*d^3 - 40*I*a^2*c*d^4 + 8*a^2*d^5)*f)) + (3*I*c^5 - 3*c^4*d + 6*I*c^3*d^2 - 6*c^2*d^3 + 3*I*c*d^4 - 3*d^5 + (9*I*c^5 - 6*c^4*d + 114*I*c^3*d^2 + 632*c^2*d^3 - 735*I*c*d^4 - 202*d^5)*e^(8*I*f*x + 8*I*e) + (30*I*c^5 - 45*c^4*d + 276*I*c^3*d^2 + 1090*c^2*d^3 - 402*I*c*d^4 + 103*d^5)*e^(6*I*f*x + 6*I*e) + (36*I*c^5 - 75*c^4*d + 192*I*c^3*d^2 + 386*c^2*d^3 + 348*I*c*d^4 + 269*d^5)*e^(4*I*f*x + 4*I*e) + (18*I*c^5 - 39*c^4*d + 36*I*c^3*d^2 - 78*c^2*d^3 + 18*I*c*d^4 - 39*d^5)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/(48*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(8*I*f*x + 8*I*e) + (96*a^2*c^8 + 192*I*a^2*c^7*d + 192*a^2*c^6*d^2 + 576*I*a^2*c^5*d^3 + 576*I*a^2*c^3*d^5 - 192*a^2*c^2*d^6 + 192*I*a^2*c*d^7 - 96*a^2*d^8)*f*e^(6*I*f*x + 6*I*e) + (48*a^2*c^8 + 192*I*a^2*c^7*d - 192*a^2*c^6*d^2 + 192*I*a^2*c^5*d^3 - 480*a^2*c^4*d^4 - 192*I*a^2*c^3*d^5 - 192*a^2*c^2*d^6 - 192*I*a^2*c*d^7 + 48*a^2*d^8)*f*e^(4*I*f*x + 4*I*e))","B",0
1136,1,3801,0,30.641882," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-24 i \, a^{3} c^{9} + 24 \, a^{3} c^{8} d - 96 i \, a^{3} c^{7} d^{2} + 96 \, a^{3} c^{6} d^{3} - 144 i \, a^{3} c^{5} d^{4} + 144 \, a^{3} c^{4} d^{5} - 96 i \, a^{3} c^{3} d^{6} + 96 \, a^{3} c^{2} d^{7} - 24 i \, a^{3} c d^{8} + 24 \, a^{3} d^{9}\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-48 i \, a^{3} c^{9} + 144 \, a^{3} c^{8} d + 384 \, a^{3} c^{6} d^{3} + 288 i \, a^{3} c^{5} d^{4} + 288 \, a^{3} c^{4} d^{5} + 384 i \, a^{3} c^{3} d^{6} + 144 i \, a^{3} c d^{8} - 48 \, a^{3} d^{9}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-24 i \, a^{3} c^{9} + 120 \, a^{3} c^{8} d + 192 i \, a^{3} c^{7} d^{2} + 336 i \, a^{3} c^{5} d^{4} - 336 \, a^{3} c^{4} d^{5} - 192 \, a^{3} c^{2} d^{7} - 120 i \, a^{3} c d^{8} + 24 \, a^{3} d^{9}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(64 i \, a^{6} c^{5} + 320 \, a^{6} c^{4} d - 640 i \, a^{6} c^{3} d^{2} - 640 \, a^{6} c^{2} d^{3} + 320 i \, a^{6} c d^{4} + 64 \, a^{6} d^{5}\right)} f^{2}}} \log\left({\left({\left({\left(16 i \, a^{3} c^{3} + 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} - 16 \, a^{3} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 i \, a^{3} c^{3} + 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} - 16 \, a^{3} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{{\left(64 i \, a^{6} c^{5} + 320 \, a^{6} c^{4} d - 640 i \, a^{6} c^{3} d^{2} - 640 \, a^{6} c^{2} d^{3} + 320 i \, a^{6} c d^{4} + 64 \, a^{6} d^{5}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(24 i \, a^{3} c^{9} - 24 \, a^{3} c^{8} d + 96 i \, a^{3} c^{7} d^{2} - 96 \, a^{3} c^{6} d^{3} + 144 i \, a^{3} c^{5} d^{4} - 144 \, a^{3} c^{4} d^{5} + 96 i \, a^{3} c^{3} d^{6} - 96 \, a^{3} c^{2} d^{7} + 24 i \, a^{3} c d^{8} - 24 \, a^{3} d^{9}\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(48 i \, a^{3} c^{9} - 144 \, a^{3} c^{8} d - 384 \, a^{3} c^{6} d^{3} - 288 i \, a^{3} c^{5} d^{4} - 288 \, a^{3} c^{4} d^{5} - 384 i \, a^{3} c^{3} d^{6} - 144 i \, a^{3} c d^{8} + 48 \, a^{3} d^{9}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 i \, a^{3} c^{9} - 120 \, a^{3} c^{8} d - 192 i \, a^{3} c^{7} d^{2} - 336 i \, a^{3} c^{5} d^{4} + 336 \, a^{3} c^{4} d^{5} + 192 \, a^{3} c^{2} d^{7} + 120 i \, a^{3} c d^{8} - 24 \, a^{3} d^{9}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(64 i \, a^{6} c^{5} + 320 \, a^{6} c^{4} d - 640 i \, a^{6} c^{3} d^{2} - 640 \, a^{6} c^{2} d^{3} + 320 i \, a^{6} c d^{4} + 64 \, a^{6} d^{5}\right)} f^{2}}} \log\left({\left({\left({\left(-16 i \, a^{3} c^{3} - 48 \, a^{3} c^{2} d + 48 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-16 i \, a^{3} c^{3} - 48 \, a^{3} c^{2} d + 48 i \, a^{3} c d^{2} + 16 \, a^{3} d^{3}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{-\frac{i}{{\left(64 i \, a^{6} c^{5} + 320 \, a^{6} c^{4} d - 640 i \, a^{6} c^{3} d^{2} - 640 \, a^{6} c^{2} d^{3} + 320 i \, a^{6} c d^{4} + 64 \, a^{6} d^{5}\right)} f^{2}}} + 2 \, {\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, c\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + {\left({\left(24 i \, a^{3} c^{9} - 24 \, a^{3} c^{8} d + 96 i \, a^{3} c^{7} d^{2} - 96 \, a^{3} c^{6} d^{3} + 144 i \, a^{3} c^{5} d^{4} - 144 \, a^{3} c^{4} d^{5} + 96 i \, a^{3} c^{3} d^{6} - 96 \, a^{3} c^{2} d^{7} + 24 i \, a^{3} c d^{8} - 24 \, a^{3} d^{9}\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(48 i \, a^{3} c^{9} - 144 \, a^{3} c^{8} d - 384 \, a^{3} c^{6} d^{3} - 288 i \, a^{3} c^{5} d^{4} - 288 \, a^{3} c^{4} d^{5} - 384 i \, a^{3} c^{3} d^{6} - 144 i \, a^{3} c d^{8} + 48 \, a^{3} d^{9}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(24 i \, a^{3} c^{9} - 120 \, a^{3} c^{8} d - 192 i \, a^{3} c^{7} d^{2} - 336 i \, a^{3} c^{5} d^{4} + 336 \, a^{3} c^{4} d^{5} + 192 \, a^{3} c^{2} d^{7} + 120 i \, a^{3} c d^{8} - 24 \, a^{3} d^{9}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{-4 i \, c^{6} + 64 \, c^{5} d + 500 i \, c^{4} d^{2} - 2560 \, c^{3} d^{3} - 8585 i \, c^{2} d^{4} + 18544 \, c d^{5} + 23104 i \, d^{6}}{{\left(256 i \, a^{6} c^{11} - 2816 \, a^{6} c^{10} d - 14080 i \, a^{6} c^{9} d^{2} + 42240 \, a^{6} c^{8} d^{3} + 84480 i \, a^{6} c^{7} d^{4} - 118272 \, a^{6} c^{6} d^{5} - 118272 i \, a^{6} c^{5} d^{6} + 84480 \, a^{6} c^{4} d^{7} + 42240 i \, a^{6} c^{3} d^{8} - 14080 \, a^{6} c^{2} d^{9} - 2816 i \, a^{6} c d^{10} + 256 \, a^{6} d^{11}\right)} f^{2}}} \log\left(-\frac{{\left(-2 i \, c^{4} + 18 \, c^{3} d + 77 i \, c^{2} d^{2} - 213 \, c d^{3} - 152 i \, d^{4} + {\left({\left(16 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 240 \, a^{3} c^{4} d^{2} - 320 i \, a^{3} c^{3} d^{3} + 240 \, a^{3} c^{2} d^{4} + 96 i \, a^{3} c d^{5} - 16 \, a^{3} d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 240 \, a^{3} c^{4} d^{2} - 320 i \, a^{3} c^{3} d^{3} + 240 \, a^{3} c^{2} d^{4} + 96 i \, a^{3} c d^{5} - 16 \, a^{3} d^{6}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{6} + 64 \, c^{5} d + 500 i \, c^{4} d^{2} - 2560 \, c^{3} d^{3} - 8585 i \, c^{2} d^{4} + 18544 \, c d^{5} + 23104 i \, d^{6}}{{\left(256 i \, a^{6} c^{11} - 2816 \, a^{6} c^{10} d - 14080 i \, a^{6} c^{9} d^{2} + 42240 \, a^{6} c^{8} d^{3} + 84480 i \, a^{6} c^{7} d^{4} - 118272 \, a^{6} c^{6} d^{5} - 118272 i \, a^{6} c^{5} d^{6} + 84480 \, a^{6} c^{4} d^{7} + 42240 i \, a^{6} c^{3} d^{8} - 14080 \, a^{6} c^{2} d^{9} - 2816 i \, a^{6} c d^{10} + 256 \, a^{6} d^{11}\right)} f^{2}}} + {\left(-2 i \, c^{4} + 16 \, c^{3} d + 61 i \, c^{2} d^{2} - 152 \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(16 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 240 \, a^{3} c^{4} d^{2} - 320 i \, a^{3} c^{3} d^{3} + 240 \, a^{3} c^{2} d^{4} + 96 i \, a^{3} c d^{5} - 16 \, a^{3} d^{6}\right)} f}\right) + {\left({\left(-24 i \, a^{3} c^{9} + 24 \, a^{3} c^{8} d - 96 i \, a^{3} c^{7} d^{2} + 96 \, a^{3} c^{6} d^{3} - 144 i \, a^{3} c^{5} d^{4} + 144 \, a^{3} c^{4} d^{5} - 96 i \, a^{3} c^{3} d^{6} + 96 \, a^{3} c^{2} d^{7} - 24 i \, a^{3} c d^{8} + 24 \, a^{3} d^{9}\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-48 i \, a^{3} c^{9} + 144 \, a^{3} c^{8} d + 384 \, a^{3} c^{6} d^{3} + 288 i \, a^{3} c^{5} d^{4} + 288 \, a^{3} c^{4} d^{5} + 384 i \, a^{3} c^{3} d^{6} + 144 i \, a^{3} c d^{8} - 48 \, a^{3} d^{9}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-24 i \, a^{3} c^{9} + 120 \, a^{3} c^{8} d + 192 i \, a^{3} c^{7} d^{2} + 336 i \, a^{3} c^{5} d^{4} - 336 \, a^{3} c^{4} d^{5} - 192 \, a^{3} c^{2} d^{7} - 120 i \, a^{3} c d^{8} + 24 \, a^{3} d^{9}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}\right)} \sqrt{\frac{-4 i \, c^{6} + 64 \, c^{5} d + 500 i \, c^{4} d^{2} - 2560 \, c^{3} d^{3} - 8585 i \, c^{2} d^{4} + 18544 \, c d^{5} + 23104 i \, d^{6}}{{\left(256 i \, a^{6} c^{11} - 2816 \, a^{6} c^{10} d - 14080 i \, a^{6} c^{9} d^{2} + 42240 \, a^{6} c^{8} d^{3} + 84480 i \, a^{6} c^{7} d^{4} - 118272 \, a^{6} c^{6} d^{5} - 118272 i \, a^{6} c^{5} d^{6} + 84480 \, a^{6} c^{4} d^{7} + 42240 i \, a^{6} c^{3} d^{8} - 14080 \, a^{6} c^{2} d^{9} - 2816 i \, a^{6} c d^{10} + 256 \, a^{6} d^{11}\right)} f^{2}}} \log\left(-\frac{{\left(-2 i \, c^{4} + 18 \, c^{3} d + 77 i \, c^{2} d^{2} - 213 \, c d^{3} - 152 i \, d^{4} - {\left({\left(16 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 240 \, a^{3} c^{4} d^{2} - 320 i \, a^{3} c^{3} d^{3} + 240 \, a^{3} c^{2} d^{4} + 96 i \, a^{3} c d^{5} - 16 \, a^{3} d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(16 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 240 \, a^{3} c^{4} d^{2} - 320 i \, a^{3} c^{3} d^{3} + 240 \, a^{3} c^{2} d^{4} + 96 i \, a^{3} c d^{5} - 16 \, a^{3} d^{6}\right)} f\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{-4 i \, c^{6} + 64 \, c^{5} d + 500 i \, c^{4} d^{2} - 2560 \, c^{3} d^{3} - 8585 i \, c^{2} d^{4} + 18544 \, c d^{5} + 23104 i \, d^{6}}{{\left(256 i \, a^{6} c^{11} - 2816 \, a^{6} c^{10} d - 14080 i \, a^{6} c^{9} d^{2} + 42240 \, a^{6} c^{8} d^{3} + 84480 i \, a^{6} c^{7} d^{4} - 118272 \, a^{6} c^{6} d^{5} - 118272 i \, a^{6} c^{5} d^{6} + 84480 \, a^{6} c^{4} d^{7} + 42240 i \, a^{6} c^{3} d^{8} - 14080 \, a^{6} c^{2} d^{9} - 2816 i \, a^{6} c d^{10} + 256 \, a^{6} d^{11}\right)} f^{2}}} + {\left(-2 i \, c^{4} + 16 \, c^{3} d + 61 i \, c^{2} d^{2} - 152 \, c d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{{\left(16 \, a^{3} c^{6} + 96 i \, a^{3} c^{5} d - 240 \, a^{3} c^{4} d^{2} - 320 i \, a^{3} c^{3} d^{3} + 240 \, a^{3} c^{2} d^{4} + 96 i \, a^{3} c d^{5} - 16 \, a^{3} d^{6}\right)} f}\right) + {\left(2 \, c^{6} + 4 i \, c^{5} d + 2 \, c^{4} d^{2} + 8 i \, c^{3} d^{3} - 2 \, c^{2} d^{4} + 4 i \, c d^{5} - 2 \, d^{6} + {\left(11 \, c^{6} + 28 i \, c^{5} d + 38 \, c^{4} d^{2} + 348 i \, c^{3} d^{3} + 1851 \, c^{2} d^{4} - 2200 i \, c d^{5} - 696 \, d^{6}\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(40 \, c^{6} + 131 i \, c^{5} d + 16 \, c^{4} d^{2} + 978 i \, c^{3} d^{3} + 3168 \, c^{2} d^{4} - 1289 i \, c d^{5} + 288 \, d^{6}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(56 \, c^{6} + 205 i \, c^{5} d - 106 \, c^{4} d^{2} + 834 i \, c^{3} d^{3} + 1068 \, c^{2} d^{4} + 1013 i \, c d^{5} + 846 \, d^{6}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(38 \, c^{6} + 133 i \, c^{5} d - 82 \, c^{4} d^{2} + 266 i \, c^{3} d^{3} - 278 \, c^{2} d^{4} + 133 i \, c d^{5} - 158 \, d^{6}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(13 \, c^{6} + 35 i \, c^{5} d + 4 \, c^{4} d^{2} + 70 i \, c^{3} d^{3} - 31 \, c^{2} d^{4} + 35 i \, c d^{5} - 22 \, d^{6}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{{\left(-96 i \, a^{3} c^{9} + 96 \, a^{3} c^{8} d - 384 i \, a^{3} c^{7} d^{2} + 384 \, a^{3} c^{6} d^{3} - 576 i \, a^{3} c^{5} d^{4} + 576 \, a^{3} c^{4} d^{5} - 384 i \, a^{3} c^{3} d^{6} + 384 \, a^{3} c^{2} d^{7} - 96 i \, a^{3} c d^{8} + 96 \, a^{3} d^{9}\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(-192 i \, a^{3} c^{9} + 576 \, a^{3} c^{8} d + 1536 \, a^{3} c^{6} d^{3} + 1152 i \, a^{3} c^{5} d^{4} + 1152 \, a^{3} c^{4} d^{5} + 1536 i \, a^{3} c^{3} d^{6} + 576 i \, a^{3} c d^{8} - 192 \, a^{3} d^{9}\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-96 i \, a^{3} c^{9} + 480 \, a^{3} c^{8} d + 768 i \, a^{3} c^{7} d^{2} + 1344 i \, a^{3} c^{5} d^{4} - 1344 \, a^{3} c^{4} d^{5} - 768 \, a^{3} c^{2} d^{7} - 480 i \, a^{3} c d^{8} + 96 \, a^{3} d^{9}\right)} f e^{\left(6 i \, f x + 6 i \, e\right)}}"," ",0,"(((-24*I*a^3*c^9 + 24*a^3*c^8*d - 96*I*a^3*c^7*d^2 + 96*a^3*c^6*d^3 - 144*I*a^3*c^5*d^4 + 144*a^3*c^4*d^5 - 96*I*a^3*c^3*d^6 + 96*a^3*c^2*d^7 - 24*I*a^3*c*d^8 + 24*a^3*d^9)*f*e^(10*I*f*x + 10*I*e) + (-48*I*a^3*c^9 + 144*a^3*c^8*d + 384*a^3*c^6*d^3 + 288*I*a^3*c^5*d^4 + 288*a^3*c^4*d^5 + 384*I*a^3*c^3*d^6 + 144*I*a^3*c*d^8 - 48*a^3*d^9)*f*e^(8*I*f*x + 8*I*e) + (-24*I*a^3*c^9 + 120*a^3*c^8*d + 192*I*a^3*c^7*d^2 + 336*I*a^3*c^5*d^4 - 336*a^3*c^4*d^5 - 192*a^3*c^2*d^7 - 120*I*a^3*c*d^8 + 24*a^3*d^9)*f*e^(6*I*f*x + 6*I*e))*sqrt(-I/((64*I*a^6*c^5 + 320*a^6*c^4*d - 640*I*a^6*c^3*d^2 - 640*a^6*c^2*d^3 + 320*I*a^6*c*d^4 + 64*a^6*d^5)*f^2))*log((((16*I*a^3*c^3 + 48*a^3*c^2*d - 48*I*a^3*c*d^2 - 16*a^3*d^3)*f*e^(2*I*f*x + 2*I*e) + (16*I*a^3*c^3 + 48*a^3*c^2*d - 48*I*a^3*c*d^2 - 16*a^3*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-I/((64*I*a^6*c^5 + 320*a^6*c^4*d - 640*I*a^6*c^3*d^2 - 640*a^6*c^2*d^3 + 320*I*a^6*c*d^4 + 64*a^6*d^5)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((24*I*a^3*c^9 - 24*a^3*c^8*d + 96*I*a^3*c^7*d^2 - 96*a^3*c^6*d^3 + 144*I*a^3*c^5*d^4 - 144*a^3*c^4*d^5 + 96*I*a^3*c^3*d^6 - 96*a^3*c^2*d^7 + 24*I*a^3*c*d^8 - 24*a^3*d^9)*f*e^(10*I*f*x + 10*I*e) + (48*I*a^3*c^9 - 144*a^3*c^8*d - 384*a^3*c^6*d^3 - 288*I*a^3*c^5*d^4 - 288*a^3*c^4*d^5 - 384*I*a^3*c^3*d^6 - 144*I*a^3*c*d^8 + 48*a^3*d^9)*f*e^(8*I*f*x + 8*I*e) + (24*I*a^3*c^9 - 120*a^3*c^8*d - 192*I*a^3*c^7*d^2 - 336*I*a^3*c^5*d^4 + 336*a^3*c^4*d^5 + 192*a^3*c^2*d^7 + 120*I*a^3*c*d^8 - 24*a^3*d^9)*f*e^(6*I*f*x + 6*I*e))*sqrt(-I/((64*I*a^6*c^5 + 320*a^6*c^4*d - 640*I*a^6*c^3*d^2 - 640*a^6*c^2*d^3 + 320*I*a^6*c*d^4 + 64*a^6*d^5)*f^2))*log((((-16*I*a^3*c^3 - 48*a^3*c^2*d + 48*I*a^3*c*d^2 + 16*a^3*d^3)*f*e^(2*I*f*x + 2*I*e) + (-16*I*a^3*c^3 - 48*a^3*c^2*d + 48*I*a^3*c*d^2 + 16*a^3*d^3)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(-I/((64*I*a^6*c^5 + 320*a^6*c^4*d - 640*I*a^6*c^3*d^2 - 640*a^6*c^2*d^3 + 320*I*a^6*c*d^4 + 64*a^6*d^5)*f^2)) + 2*(c - I*d)*e^(2*I*f*x + 2*I*e) + 2*c)*e^(-2*I*f*x - 2*I*e)) + ((24*I*a^3*c^9 - 24*a^3*c^8*d + 96*I*a^3*c^7*d^2 - 96*a^3*c^6*d^3 + 144*I*a^3*c^5*d^4 - 144*a^3*c^4*d^5 + 96*I*a^3*c^3*d^6 - 96*a^3*c^2*d^7 + 24*I*a^3*c*d^8 - 24*a^3*d^9)*f*e^(10*I*f*x + 10*I*e) + (48*I*a^3*c^9 - 144*a^3*c^8*d - 384*a^3*c^6*d^3 - 288*I*a^3*c^5*d^4 - 288*a^3*c^4*d^5 - 384*I*a^3*c^3*d^6 - 144*I*a^3*c*d^8 + 48*a^3*d^9)*f*e^(8*I*f*x + 8*I*e) + (24*I*a^3*c^9 - 120*a^3*c^8*d - 192*I*a^3*c^7*d^2 - 336*I*a^3*c^5*d^4 + 336*a^3*c^4*d^5 + 192*a^3*c^2*d^7 + 120*I*a^3*c*d^8 - 24*a^3*d^9)*f*e^(6*I*f*x + 6*I*e))*sqrt((-4*I*c^6 + 64*c^5*d + 500*I*c^4*d^2 - 2560*c^3*d^3 - 8585*I*c^2*d^4 + 18544*c*d^5 + 23104*I*d^6)/((256*I*a^6*c^11 - 2816*a^6*c^10*d - 14080*I*a^6*c^9*d^2 + 42240*a^6*c^8*d^3 + 84480*I*a^6*c^7*d^4 - 118272*a^6*c^6*d^5 - 118272*I*a^6*c^5*d^6 + 84480*a^6*c^4*d^7 + 42240*I*a^6*c^3*d^8 - 14080*a^6*c^2*d^9 - 2816*I*a^6*c*d^10 + 256*a^6*d^11)*f^2))*log(-(-2*I*c^4 + 18*c^3*d + 77*I*c^2*d^2 - 213*c*d^3 - 152*I*d^4 + ((16*a^3*c^6 + 96*I*a^3*c^5*d - 240*a^3*c^4*d^2 - 320*I*a^3*c^3*d^3 + 240*a^3*c^2*d^4 + 96*I*a^3*c*d^5 - 16*a^3*d^6)*f*e^(2*I*f*x + 2*I*e) + (16*a^3*c^6 + 96*I*a^3*c^5*d - 240*a^3*c^4*d^2 - 320*I*a^3*c^3*d^3 + 240*a^3*c^2*d^4 + 96*I*a^3*c*d^5 - 16*a^3*d^6)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^6 + 64*c^5*d + 500*I*c^4*d^2 - 2560*c^3*d^3 - 8585*I*c^2*d^4 + 18544*c*d^5 + 23104*I*d^6)/((256*I*a^6*c^11 - 2816*a^6*c^10*d - 14080*I*a^6*c^9*d^2 + 42240*a^6*c^8*d^3 + 84480*I*a^6*c^7*d^4 - 118272*a^6*c^6*d^5 - 118272*I*a^6*c^5*d^6 + 84480*a^6*c^4*d^7 + 42240*I*a^6*c^3*d^8 - 14080*a^6*c^2*d^9 - 2816*I*a^6*c*d^10 + 256*a^6*d^11)*f^2)) + (-2*I*c^4 + 16*c^3*d + 61*I*c^2*d^2 - 152*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((16*a^3*c^6 + 96*I*a^3*c^5*d - 240*a^3*c^4*d^2 - 320*I*a^3*c^3*d^3 + 240*a^3*c^2*d^4 + 96*I*a^3*c*d^5 - 16*a^3*d^6)*f)) + ((-24*I*a^3*c^9 + 24*a^3*c^8*d - 96*I*a^3*c^7*d^2 + 96*a^3*c^6*d^3 - 144*I*a^3*c^5*d^4 + 144*a^3*c^4*d^5 - 96*I*a^3*c^3*d^6 + 96*a^3*c^2*d^7 - 24*I*a^3*c*d^8 + 24*a^3*d^9)*f*e^(10*I*f*x + 10*I*e) + (-48*I*a^3*c^9 + 144*a^3*c^8*d + 384*a^3*c^6*d^3 + 288*I*a^3*c^5*d^4 + 288*a^3*c^4*d^5 + 384*I*a^3*c^3*d^6 + 144*I*a^3*c*d^8 - 48*a^3*d^9)*f*e^(8*I*f*x + 8*I*e) + (-24*I*a^3*c^9 + 120*a^3*c^8*d + 192*I*a^3*c^7*d^2 + 336*I*a^3*c^5*d^4 - 336*a^3*c^4*d^5 - 192*a^3*c^2*d^7 - 120*I*a^3*c*d^8 + 24*a^3*d^9)*f*e^(6*I*f*x + 6*I*e))*sqrt((-4*I*c^6 + 64*c^5*d + 500*I*c^4*d^2 - 2560*c^3*d^3 - 8585*I*c^2*d^4 + 18544*c*d^5 + 23104*I*d^6)/((256*I*a^6*c^11 - 2816*a^6*c^10*d - 14080*I*a^6*c^9*d^2 + 42240*a^6*c^8*d^3 + 84480*I*a^6*c^7*d^4 - 118272*a^6*c^6*d^5 - 118272*I*a^6*c^5*d^6 + 84480*a^6*c^4*d^7 + 42240*I*a^6*c^3*d^8 - 14080*a^6*c^2*d^9 - 2816*I*a^6*c*d^10 + 256*a^6*d^11)*f^2))*log(-(-2*I*c^4 + 18*c^3*d + 77*I*c^2*d^2 - 213*c*d^3 - 152*I*d^4 - ((16*a^3*c^6 + 96*I*a^3*c^5*d - 240*a^3*c^4*d^2 - 320*I*a^3*c^3*d^3 + 240*a^3*c^2*d^4 + 96*I*a^3*c*d^5 - 16*a^3*d^6)*f*e^(2*I*f*x + 2*I*e) + (16*a^3*c^6 + 96*I*a^3*c^5*d - 240*a^3*c^4*d^2 - 320*I*a^3*c^3*d^3 + 240*a^3*c^2*d^4 + 96*I*a^3*c*d^5 - 16*a^3*d^6)*f)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt((-4*I*c^6 + 64*c^5*d + 500*I*c^4*d^2 - 2560*c^3*d^3 - 8585*I*c^2*d^4 + 18544*c*d^5 + 23104*I*d^6)/((256*I*a^6*c^11 - 2816*a^6*c^10*d - 14080*I*a^6*c^9*d^2 + 42240*a^6*c^8*d^3 + 84480*I*a^6*c^7*d^4 - 118272*a^6*c^6*d^5 - 118272*I*a^6*c^5*d^6 + 84480*a^6*c^4*d^7 + 42240*I*a^6*c^3*d^8 - 14080*a^6*c^2*d^9 - 2816*I*a^6*c*d^10 + 256*a^6*d^11)*f^2)) + (-2*I*c^4 + 16*c^3*d + 61*I*c^2*d^2 - 152*c*d^3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)/((16*a^3*c^6 + 96*I*a^3*c^5*d - 240*a^3*c^4*d^2 - 320*I*a^3*c^3*d^3 + 240*a^3*c^2*d^4 + 96*I*a^3*c*d^5 - 16*a^3*d^6)*f)) + (2*c^6 + 4*I*c^5*d + 2*c^4*d^2 + 8*I*c^3*d^3 - 2*c^2*d^4 + 4*I*c*d^5 - 2*d^6 + (11*c^6 + 28*I*c^5*d + 38*c^4*d^2 + 348*I*c^3*d^3 + 1851*c^2*d^4 - 2200*I*c*d^5 - 696*d^6)*e^(10*I*f*x + 10*I*e) + (40*c^6 + 131*I*c^5*d + 16*c^4*d^2 + 978*I*c^3*d^3 + 3168*c^2*d^4 - 1289*I*c*d^5 + 288*d^6)*e^(8*I*f*x + 8*I*e) + (56*c^6 + 205*I*c^5*d - 106*c^4*d^2 + 834*I*c^3*d^3 + 1068*c^2*d^4 + 1013*I*c*d^5 + 846*d^6)*e^(6*I*f*x + 6*I*e) + (38*c^6 + 133*I*c^5*d - 82*c^4*d^2 + 266*I*c^3*d^3 - 278*c^2*d^4 + 133*I*c*d^5 - 158*d^6)*e^(4*I*f*x + 4*I*e) + (13*c^6 + 35*I*c^5*d + 4*c^4*d^2 + 70*I*c^3*d^3 - 31*c^2*d^4 + 35*I*c*d^5 - 22*d^6)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)))/((-96*I*a^3*c^9 + 96*a^3*c^8*d - 384*I*a^3*c^7*d^2 + 384*a^3*c^6*d^3 - 576*I*a^3*c^5*d^4 + 576*a^3*c^4*d^5 - 384*I*a^3*c^3*d^6 + 384*a^3*c^2*d^7 - 96*I*a^3*c*d^8 + 96*a^3*d^9)*f*e^(10*I*f*x + 10*I*e) + (-192*I*a^3*c^9 + 576*a^3*c^8*d + 1536*a^3*c^6*d^3 + 1152*I*a^3*c^5*d^4 + 1152*a^3*c^4*d^5 + 1536*I*a^3*c^3*d^6 + 576*I*a^3*c*d^8 - 192*a^3*d^9)*f*e^(8*I*f*x + 8*I*e) + (-96*I*a^3*c^9 + 480*a^3*c^8*d + 768*I*a^3*c^7*d^2 + 1344*I*a^3*c^5*d^4 - 1344*a^3*c^4*d^5 - 768*a^3*c^2*d^7 - 480*I*a^3*c*d^8 + 96*a^3*d^9)*f*e^(6*I*f*x + 6*I*e))","B",0
1137,1,1031,0,0.527373," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left({\left(a^{2} c - 11 i \, a^{2} d\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(a^{2} c - 7 i \, a^{2} d\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{i \, a^{5} c^{4} - 20 \, a^{5} c^{3} d - 54 i \, a^{5} c^{2} d^{2} - 460 \, a^{5} c d^{3} + 529 i \, a^{5} d^{4}}{d^{3} f^{2}}} \log\left(\frac{{\left(2 i \, d^{2} f \sqrt{\frac{i \, a^{5} c^{4} - 20 \, a^{5} c^{3} d - 54 i \, a^{5} c^{2} d^{2} - 460 \, a^{5} c d^{3} + 529 i \, a^{5} d^{4}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(a^{2} c^{2} + 10 i \, a^{2} c d + 23 \, a^{2} d^{2} + {\left(a^{2} c^{2} + 10 i \, a^{2} c d + 23 \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a^{2} c^{2} + 10 i \, a^{2} c d + 23 \, a^{2} d^{2}}\right) - {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{i \, a^{5} c^{4} - 20 \, a^{5} c^{3} d - 54 i \, a^{5} c^{2} d^{2} - 460 \, a^{5} c d^{3} + 529 i \, a^{5} d^{4}}{d^{3} f^{2}}} \log\left(\frac{{\left(-2 i \, d^{2} f \sqrt{\frac{i \, a^{5} c^{4} - 20 \, a^{5} c^{3} d - 54 i \, a^{5} c^{2} d^{2} - 460 \, a^{5} c d^{3} + 529 i \, a^{5} d^{4}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(a^{2} c^{2} + 10 i \, a^{2} c d + 23 \, a^{2} d^{2} + {\left(a^{2} c^{2} + 10 i \, a^{2} c d + 23 \, a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a^{2} c^{2} + 10 i \, a^{2} c d + 23 \, a^{2} d^{2}}\right) - 4 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{32 \, a^{5} c - 32 i \, a^{5} d}{f^{2}}} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + i \, f \sqrt{-\frac{32 \, a^{5} c - 32 i \, a^{5} d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right) + 4 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{32 \, a^{5} c - 32 i \, a^{5} d}{f^{2}}} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - i \, f \sqrt{-\frac{32 \, a^{5} c - 32 i \, a^{5} d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right)}{8 \, {\left(d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"-1/8*(2*sqrt(2)*((a^2*c - 11*I*a^2*d)*e^(3*I*f*x + 3*I*e) + (a^2*c - 7*I*a^2*d)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + (d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((I*a^5*c^4 - 20*a^5*c^3*d - 54*I*a^5*c^2*d^2 - 460*a^5*c*d^3 + 529*I*a^5*d^4)/(d^3*f^2))*log((2*I*d^2*f*sqrt((I*a^5*c^4 - 20*a^5*c^3*d - 54*I*a^5*c^2*d^2 - 460*a^5*c*d^3 + 529*I*a^5*d^4)/(d^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*(a^2*c^2 + 10*I*a^2*c*d + 23*a^2*d^2 + (a^2*c^2 + 10*I*a^2*c*d + 23*a^2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^2*c^2 + 10*I*a^2*c*d + 23*a^2*d^2)) - (d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((I*a^5*c^4 - 20*a^5*c^3*d - 54*I*a^5*c^2*d^2 - 460*a^5*c*d^3 + 529*I*a^5*d^4)/(d^3*f^2))*log((-2*I*d^2*f*sqrt((I*a^5*c^4 - 20*a^5*c^3*d - 54*I*a^5*c^2*d^2 - 460*a^5*c*d^3 + 529*I*a^5*d^4)/(d^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*(a^2*c^2 + 10*I*a^2*c*d + 23*a^2*d^2 + (a^2*c^2 + 10*I*a^2*c*d + 23*a^2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a^2*c^2 + 10*I*a^2*c*d + 23*a^2*d^2)) - 4*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(32*a^5*c - 32*I*a^5*d)/f^2)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + I*f*sqrt(-(32*a^5*c - 32*I*a^5*d)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/a^2) + 4*(d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(32*a^5*c - 32*I*a^5*d)/f^2)*log(1/4*(4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - I*f*sqrt(-(32*a^5*c - 32*I*a^5*d)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/a^2))/(d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
1138,1,736,0,0.476635," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} a \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(i \, f x + i \, e\right)} - f \sqrt{\frac{-i \, a^{3} c^{2} - 6 \, a^{3} c d + 9 i \, a^{3} d^{2}}{d f^{2}}} \log\left(\frac{{\left(2 i \, d f \sqrt{\frac{-i \, a^{3} c^{2} - 6 \, a^{3} c d + 9 i \, a^{3} d^{2}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(i \, a c + 3 \, a d + {\left(i \, a c + 3 \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{i \, a c + 3 \, a d}\right) + f \sqrt{\frac{-i \, a^{3} c^{2} - 6 \, a^{3} c d + 9 i \, a^{3} d^{2}}{d f^{2}}} \log\left(\frac{{\left(-2 i \, d f \sqrt{\frac{-i \, a^{3} c^{2} - 6 \, a^{3} c d + 9 i \, a^{3} d^{2}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(i \, a c + 3 \, a d + {\left(i \, a c + 3 \, a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{i \, a c + 3 \, a d}\right) + f \sqrt{-\frac{8 \, a^{3} c - 8 i \, a^{3} d}{f^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + i \, f \sqrt{-\frac{8 \, a^{3} c - 8 i \, a^{3} d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right) - f \sqrt{-\frac{8 \, a^{3} c - 8 i \, a^{3} d}{f^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - i \, f \sqrt{-\frac{8 \, a^{3} c - 8 i \, a^{3} d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right)}{2 \, f}"," ",0,"1/2*(2*I*sqrt(2)*a*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*e^(I*f*x + I*e) - f*sqrt((-I*a^3*c^2 - 6*a^3*c*d + 9*I*a^3*d^2)/(d*f^2))*log((2*I*d*f*sqrt((-I*a^3*c^2 - 6*a^3*c*d + 9*I*a^3*d^2)/(d*f^2))*e^(I*f*x + I*e) + sqrt(2)*(I*a*c + 3*a*d + (I*a*c + 3*a*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(I*a*c + 3*a*d)) + f*sqrt((-I*a^3*c^2 - 6*a^3*c*d + 9*I*a^3*d^2)/(d*f^2))*log((-2*I*d*f*sqrt((-I*a^3*c^2 - 6*a^3*c*d + 9*I*a^3*d^2)/(d*f^2))*e^(I*f*x + I*e) + sqrt(2)*(I*a*c + 3*a*d + (I*a*c + 3*a*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(I*a*c + 3*a*d)) + f*sqrt(-(8*a^3*c - 8*I*a^3*d)/f^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + I*f*sqrt(-(8*a^3*c - 8*I*a^3*d)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/a) - f*sqrt(-(8*a^3*c - 8*I*a^3*d)/f^2)*log(1/2*(2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - I*f*sqrt(-(8*a^3*c - 8*I*a^3*d)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/a))/f","B",0
1139,1,477,0,0.454947," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{4 i \, a d}{f^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} + i \, f \sqrt{\frac{4 i \, a d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right) + \frac{1}{2} \, \sqrt{\frac{4 i \, a d}{f^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} - i \, f \sqrt{\frac{4 i \, a d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right) + \frac{1}{2} \, \sqrt{-\frac{2 \, a c - 2 i \, a d}{f^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} + i \, f \sqrt{-\frac{2 \, a c - 2 i \, a d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right) - \frac{1}{2} \, \sqrt{-\frac{2 \, a c - 2 i \, a d}{f^{2}}} \log\left({\left(\sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} - i \, f \sqrt{-\frac{2 \, a c - 2 i \, a d}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right)"," ",0,"-1/2*sqrt(4*I*a*d/f^2)*log((sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1) + I*f*sqrt(4*I*a*d/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)) + 1/2*sqrt(4*I*a*d/f^2)*log((sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1) - I*f*sqrt(4*I*a*d/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)) + 1/2*sqrt(-(2*a*c - 2*I*a*d)/f^2)*log((sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1) + I*f*sqrt(-(2*a*c - 2*I*a*d)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)) - 1/2*sqrt(-(2*a*c - 2*I*a*d)/f^2)*log((sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1) - I*f*sqrt(-(2*a*c - 2*I*a*d)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e))","B",0
1140,1,351,0,0.554909," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} a f \sqrt{-\frac{c - i \, d}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(i \, \sqrt{2} a f \sqrt{-\frac{c - i \, d}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - \sqrt{2} a f \sqrt{-\frac{c - i \, d}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(-i \, \sqrt{2} a f \sqrt{-\frac{c - i \, d}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(2 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a f}"," ",0,"1/4*(sqrt(2)*a*f*sqrt(-(c - I*d)/(a*f^2))*e^(I*f*x + I*e)*log(I*sqrt(2)*a*f*sqrt(-(c - I*d)/(a*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - sqrt(2)*a*f*sqrt(-(c - I*d)/(a*f^2))*e^(I*f*x + I*e)*log(-I*sqrt(2)*a*f*sqrt(-(c - I*d)/(a*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(2*I*e^(2*I*f*x + 2*I*e) + 2*I))*e^(-I*f*x - I*e)/(a*f)","B",0
1141,1,419,0,0.511744," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} {\left(i \, a^{2} c - a^{2} d\right)} f \sqrt{-\frac{c - i \, d}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(2 i \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c - i \, d}{a^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(-i \, a^{2} c + a^{2} d\right)} f \sqrt{-\frac{c - i \, d}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-2 i \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c - i \, d}{a^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - \sqrt{2} {\left(2 \, {\left(2 \, c + i \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(5 \, c + 3 i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{12 \, {\left(i \, a^{2} c - a^{2} d\right)} f}"," ",0,"1/12*(3*sqrt(1/2)*(I*a^2*c - a^2*d)*f*sqrt(-(c - I*d)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(2*I*sqrt(1/2)*a^2*f*sqrt(-(c - I*d)/(a^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + 3*sqrt(1/2)*(-I*a^2*c + a^2*d)*f*sqrt(-(c - I*d)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(-2*I*sqrt(1/2)*a^2*f*sqrt(-(c - I*d)/(a^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - sqrt(2)*(2*(2*c + I*d)*e^(4*I*f*x + 4*I*e) + (5*c + 3*I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-3*I*f*x - 3*I*e)/((I*a^2*c - a^2*d)*f)","B",0
1142,1,500,0,0.544902," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f \sqrt{-\frac{c - i \, d}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(2 i \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c - i \, d}{a^{5} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - 15 \, \sqrt{\frac{1}{2}} {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f \sqrt{-\frac{c - i \, d}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(-2 i \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c - i \, d}{a^{5} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - \sqrt{2} {\left(-3 i \, c^{2} + 6 \, c d + 3 i \, d^{2} + {\left(-23 i \, c^{2} + 34 \, c d + 3 i \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-34 i \, c^{2} + 54 \, c d + 12 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-14 i \, c^{2} + 26 \, c d + 12 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{120 \, {\left(a^{3} c^{2} + 2 i \, a^{3} c d - a^{3} d^{2}\right)} f}"," ",0,"1/120*(15*sqrt(1/2)*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*sqrt(-(c - I*d)/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(2*I*sqrt(1/2)*a^3*f*sqrt(-(c - I*d)/(a^5*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - 15*sqrt(1/2)*(a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f*sqrt(-(c - I*d)/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(-2*I*sqrt(1/2)*a^3*f*sqrt(-(c - I*d)/(a^5*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - sqrt(2)*(-3*I*c^2 + 6*c*d + 3*I*d^2 + (-23*I*c^2 + 34*c*d + 3*I*d^2)*e^(6*I*f*x + 6*I*e) + (-34*I*c^2 + 54*c*d + 12*I*d^2)*e^(4*I*f*x + 4*I*e) + (-14*I*c^2 + 26*c*d + 12*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-5*I*f*x - 5*I*e)/((a^3*c^2 + 2*I*a^3*c*d - a^3*d^2)*f)","B",0
1143,1,1467,0,0.609880," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left({\left(3 \, a^{2} c^{2} - 82 i \, a^{2} c d - 91 \, a^{2} d^{2}\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + 2 \, {\left(3 \, a^{2} c^{2} - 68 i \, a^{2} c d - 49 \, a^{2} d^{2}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + 3 \, {\left(a^{2} c^{2} - 18 i \, a^{2} c d - 13 \, a^{2} d^{2}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - 3 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{i \, a^{5} c^{6} - 30 \, a^{5} c^{5} d - 87 i \, a^{5} c^{4} d^{2} - 1980 \, a^{5} c^{3} d^{3} + 6111 i \, a^{5} c^{2} d^{4} + 6210 \, a^{5} c d^{5} - 2025 i \, a^{5} d^{6}}{d^{3} f^{2}}} \log\left(\frac{{\left(2 \, d^{2} f \sqrt{\frac{i \, a^{5} c^{6} - 30 \, a^{5} c^{5} d - 87 i \, a^{5} c^{4} d^{2} - 1980 \, a^{5} c^{3} d^{3} + 6111 i \, a^{5} c^{2} d^{4} + 6210 \, a^{5} c d^{5} - 2025 i \, a^{5} d^{6}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(i \, a^{2} c^{3} - 15 \, a^{2} c^{2} d + 69 i \, a^{2} c d^{2} + 45 \, a^{2} d^{3} + {\left(i \, a^{2} c^{3} - 15 \, a^{2} c^{2} d + 69 i \, a^{2} c d^{2} + 45 \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{i \, a^{2} c^{3} - 15 \, a^{2} c^{2} d + 69 i \, a^{2} c d^{2} + 45 \, a^{2} d^{3}}\right) + 3 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{i \, a^{5} c^{6} - 30 \, a^{5} c^{5} d - 87 i \, a^{5} c^{4} d^{2} - 1980 \, a^{5} c^{3} d^{3} + 6111 i \, a^{5} c^{2} d^{4} + 6210 \, a^{5} c d^{5} - 2025 i \, a^{5} d^{6}}{d^{3} f^{2}}} \log\left(-\frac{{\left(2 \, d^{2} f \sqrt{\frac{i \, a^{5} c^{6} - 30 \, a^{5} c^{5} d - 87 i \, a^{5} c^{4} d^{2} - 1980 \, a^{5} c^{3} d^{3} + 6111 i \, a^{5} c^{2} d^{4} + 6210 \, a^{5} c d^{5} - 2025 i \, a^{5} d^{6}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(i \, a^{2} c^{3} - 15 \, a^{2} c^{2} d + 69 i \, a^{2} c d^{2} + 45 \, a^{2} d^{3} + {\left(i \, a^{2} c^{3} - 15 \, a^{2} c^{2} d + 69 i \, a^{2} c d^{2} + 45 \, a^{2} d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{i \, a^{2} c^{3} - 15 \, a^{2} c^{2} d + 69 i \, a^{2} c d^{2} + 45 \, a^{2} d^{3}}\right) - 24 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{32 \, a^{5} c^{3} - 96 i \, a^{5} c^{2} d - 96 \, a^{5} c d^{2} + 32 i \, a^{5} d^{3}}{f^{2}}} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(-i \, a^{2} c - a^{2} d + {\left(-i \, a^{2} c - a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + f \sqrt{-\frac{32 \, a^{5} c^{3} - 96 i \, a^{5} c^{2} d - 96 \, a^{5} c d^{2} + 32 i \, a^{5} d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, {\left(-i \, a^{2} c - a^{2} d\right)}}\right) + 24 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{32 \, a^{5} c^{3} - 96 i \, a^{5} c^{2} d - 96 \, a^{5} c d^{2} + 32 i \, a^{5} d^{3}}{f^{2}}} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(-i \, a^{2} c - a^{2} d + {\left(-i \, a^{2} c - a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - f \sqrt{-\frac{32 \, a^{5} c^{3} - 96 i \, a^{5} c^{2} d - 96 \, a^{5} c d^{2} + 32 i \, a^{5} d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, {\left(-i \, a^{2} c - a^{2} d\right)}}\right)}{48 \, {\left(d f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"-1/48*(2*sqrt(2)*((3*a^2*c^2 - 82*I*a^2*c*d - 91*a^2*d^2)*e^(5*I*f*x + 5*I*e) + 2*(3*a^2*c^2 - 68*I*a^2*c*d - 49*a^2*d^2)*e^(3*I*f*x + 3*I*e) + 3*(a^2*c^2 - 18*I*a^2*c*d - 13*a^2*d^2)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - 3*(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((I*a^5*c^6 - 30*a^5*c^5*d - 87*I*a^5*c^4*d^2 - 1980*a^5*c^3*d^3 + 6111*I*a^5*c^2*d^4 + 6210*a^5*c*d^5 - 2025*I*a^5*d^6)/(d^3*f^2))*log((2*d^2*f*sqrt((I*a^5*c^6 - 30*a^5*c^5*d - 87*I*a^5*c^4*d^2 - 1980*a^5*c^3*d^3 + 6111*I*a^5*c^2*d^4 + 6210*a^5*c*d^5 - 2025*I*a^5*d^6)/(d^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*(I*a^2*c^3 - 15*a^2*c^2*d + 69*I*a^2*c*d^2 + 45*a^2*d^3 + (I*a^2*c^3 - 15*a^2*c^2*d + 69*I*a^2*c*d^2 + 45*a^2*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(I*a^2*c^3 - 15*a^2*c^2*d + 69*I*a^2*c*d^2 + 45*a^2*d^3)) + 3*(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((I*a^5*c^6 - 30*a^5*c^5*d - 87*I*a^5*c^4*d^2 - 1980*a^5*c^3*d^3 + 6111*I*a^5*c^2*d^4 + 6210*a^5*c*d^5 - 2025*I*a^5*d^6)/(d^3*f^2))*log(-(2*d^2*f*sqrt((I*a^5*c^6 - 30*a^5*c^5*d - 87*I*a^5*c^4*d^2 - 1980*a^5*c^3*d^3 + 6111*I*a^5*c^2*d^4 + 6210*a^5*c*d^5 - 2025*I*a^5*d^6)/(d^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*(I*a^2*c^3 - 15*a^2*c^2*d + 69*I*a^2*c*d^2 + 45*a^2*d^3 + (I*a^2*c^3 - 15*a^2*c^2*d + 69*I*a^2*c*d^2 + 45*a^2*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(I*a^2*c^3 - 15*a^2*c^2*d + 69*I*a^2*c*d^2 + 45*a^2*d^3)) - 24*(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(32*a^5*c^3 - 96*I*a^5*c^2*d - 96*a^5*c*d^2 + 32*I*a^5*d^3)/f^2)*log(1/4*(4*sqrt(2)*(-I*a^2*c - a^2*d + (-I*a^2*c - a^2*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + f*sqrt(-(32*a^5*c^3 - 96*I*a^5*c^2*d - 96*a^5*c*d^2 + 32*I*a^5*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(-I*a^2*c - a^2*d)) + 24*(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(32*a^5*c^3 - 96*I*a^5*c^2*d - 96*a^5*c*d^2 + 32*I*a^5*d^3)/f^2)*log(1/4*(4*sqrt(2)*(-I*a^2*c - a^2*d + (-I*a^2*c - a^2*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - f*sqrt(-(32*a^5*c^3 - 96*I*a^5*c^2*d - 96*a^5*c*d^2 + 32*I*a^5*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(-I*a^2*c - a^2*d)))/(d*f*e^(4*I*f*x + 4*I*e) + 2*d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
1144,1,1103,0,0.634917," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(5 i \, a c + 7 \, a d\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(5 i \, a c + 3 \, a d\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-9 i \, a^{3} c^{4} - 108 \, a^{3} c^{3} d + 390 i \, a^{3} c^{2} d^{2} + 396 \, a^{3} c d^{3} - 121 i \, a^{3} d^{4}}{d f^{2}}} \log\left(\frac{{\left(2 \, d f \sqrt{\frac{-9 i \, a^{3} c^{4} - 108 \, a^{3} c^{3} d + 390 i \, a^{3} c^{2} d^{2} + 396 \, a^{3} c d^{3} - 121 i \, a^{3} d^{4}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(3 \, a c^{2} - 18 i \, a c d - 11 \, a d^{2} + {\left(3 \, a c^{2} - 18 i \, a c d - 11 \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{3 \, a c^{2} - 18 i \, a c d - 11 \, a d^{2}}\right) + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-9 i \, a^{3} c^{4} - 108 \, a^{3} c^{3} d + 390 i \, a^{3} c^{2} d^{2} + 396 \, a^{3} c d^{3} - 121 i \, a^{3} d^{4}}{d f^{2}}} \log\left(-\frac{{\left(2 \, d f \sqrt{\frac{-9 i \, a^{3} c^{4} - 108 \, a^{3} c^{3} d + 390 i \, a^{3} c^{2} d^{2} + 396 \, a^{3} c d^{3} - 121 i \, a^{3} d^{4}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(3 \, a c^{2} - 18 i \, a c d - 11 \, a d^{2} + {\left(3 \, a c^{2} - 18 i \, a c d - 11 \, a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{3 \, a c^{2} - 18 i \, a c d - 11 \, a d^{2}}\right) + 4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{8 \, a^{3} c^{3} - 24 i \, a^{3} c^{2} d - 24 \, a^{3} c d^{2} + 8 i \, a^{3} d^{3}}{f^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(-i \, a c - a d + {\left(-i \, a c - a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + f \sqrt{-\frac{8 \, a^{3} c^{3} - 24 i \, a^{3} c^{2} d - 24 \, a^{3} c d^{2} + 8 i \, a^{3} d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, {\left(-i \, a c - a d\right)}}\right) - 4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{8 \, a^{3} c^{3} - 24 i \, a^{3} c^{2} d - 24 \, a^{3} c d^{2} + 8 i \, a^{3} d^{3}}{f^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(-i \, a c - a d + {\left(-i \, a c - a d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - f \sqrt{-\frac{8 \, a^{3} c^{3} - 24 i \, a^{3} c^{2} d - 24 \, a^{3} c d^{2} + 8 i \, a^{3} d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, {\left(-i \, a c - a d\right)}}\right)}{8 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/8*(2*sqrt(2)*((5*I*a*c + 7*a*d)*e^(3*I*f*x + 3*I*e) + (5*I*a*c + 3*a*d)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - (f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-9*I*a^3*c^4 - 108*a^3*c^3*d + 390*I*a^3*c^2*d^2 + 396*a^3*c*d^3 - 121*I*a^3*d^4)/(d*f^2))*log((2*d*f*sqrt((-9*I*a^3*c^4 - 108*a^3*c^3*d + 390*I*a^3*c^2*d^2 + 396*a^3*c*d^3 - 121*I*a^3*d^4)/(d*f^2))*e^(I*f*x + I*e) + sqrt(2)*(3*a*c^2 - 18*I*a*c*d - 11*a*d^2 + (3*a*c^2 - 18*I*a*c*d - 11*a*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(3*a*c^2 - 18*I*a*c*d - 11*a*d^2)) + (f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-9*I*a^3*c^4 - 108*a^3*c^3*d + 390*I*a^3*c^2*d^2 + 396*a^3*c*d^3 - 121*I*a^3*d^4)/(d*f^2))*log(-(2*d*f*sqrt((-9*I*a^3*c^4 - 108*a^3*c^3*d + 390*I*a^3*c^2*d^2 + 396*a^3*c*d^3 - 121*I*a^3*d^4)/(d*f^2))*e^(I*f*x + I*e) - sqrt(2)*(3*a*c^2 - 18*I*a*c*d - 11*a*d^2 + (3*a*c^2 - 18*I*a*c*d - 11*a*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(3*a*c^2 - 18*I*a*c*d - 11*a*d^2)) + 4*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(8*a^3*c^3 - 24*I*a^3*c^2*d - 24*a^3*c*d^2 + 8*I*a^3*d^3)/f^2)*log(1/2*(2*sqrt(2)*(-I*a*c - a*d + (-I*a*c - a*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + f*sqrt(-(8*a^3*c^3 - 24*I*a^3*c^2*d - 24*a^3*c*d^2 + 8*I*a^3*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(-I*a*c - a*d)) - 4*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(8*a^3*c^3 - 24*I*a^3*c^2*d - 24*a^3*c*d^2 + 8*I*a^3*d^3)/f^2)*log(1/2*(2*sqrt(2)*(-I*a*c - a*d + (-I*a*c - a*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - f*sqrt(-(8*a^3*c^3 - 24*I*a^3*c^2*d - 24*a^3*c*d^2 + 8*I*a^3*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(-I*a*c - a*d)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
1145,1,759,0,0.725567," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} d \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(i \, f x + i \, e\right)} + f \sqrt{\frac{9 i \, a c^{2} d + 6 \, a c d^{2} - i \, a d^{3}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(3 i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + 2 \, f \sqrt{\frac{9 i \, a c^{2} d + 6 \, a c d^{2} - i \, a d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{3 i \, c + d}\right) - f \sqrt{\frac{9 i \, a c^{2} d + 6 \, a c d^{2} - i \, a d^{3}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(3 i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - 2 \, f \sqrt{\frac{9 i \, a c^{2} d + 6 \, a c d^{2} - i \, a d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{3 i \, c + d}\right) - f \sqrt{-\frac{2 \, a c^{3} - 6 i \, a c^{2} d - 6 \, a c d^{2} + 2 i \, a d^{3}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + f \sqrt{-\frac{2 \, a c^{3} - 6 i \, a c^{2} d - 6 \, a c d^{2} + 2 i \, a d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{i \, c + d}\right) + f \sqrt{-\frac{2 \, a c^{3} - 6 i \, a c^{2} d - 6 \, a c d^{2} + 2 i \, a d^{3}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - f \sqrt{-\frac{2 \, a c^{3} - 6 i \, a c^{2} d - 6 \, a c d^{2} + 2 i \, a d^{3}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{i \, c + d}\right)}{2 \, f}"," ",0,"1/2*(2*sqrt(2)*d*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*e^(I*f*x + I*e) + f*sqrt((9*I*a*c^2*d + 6*a*c*d^2 - I*a*d^3)/f^2)*log((sqrt(2)*((3*I*c + d)*e^(2*I*f*x + 2*I*e) + 3*I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + 2*f*sqrt((9*I*a*c^2*d + 6*a*c*d^2 - I*a*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(3*I*c + d)) - f*sqrt((9*I*a*c^2*d + 6*a*c*d^2 - I*a*d^3)/f^2)*log((sqrt(2)*((3*I*c + d)*e^(2*I*f*x + 2*I*e) + 3*I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - 2*f*sqrt((9*I*a*c^2*d + 6*a*c*d^2 - I*a*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(3*I*c + d)) - f*sqrt(-(2*a*c^3 - 6*I*a*c^2*d - 6*a*c*d^2 + 2*I*a*d^3)/f^2)*log((sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + f*sqrt(-(2*a*c^3 - 6*I*a*c^2*d - 6*a*c*d^2 + 2*I*a*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(I*c + d)) + f*sqrt(-(2*a*c^3 - 6*I*a*c^2*d - 6*a*c*d^2 + 2*I*a*d^3)/f^2)*log((sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - f*sqrt(-(2*a*c^3 - 6*I*a*c^2*d - 6*a*c*d^2 + 2*I*a*d^3)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(I*c + d)))/f","B",0
1146,1,895,0,0.638664," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a f \sqrt{-\frac{4 i \, d^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left(4 \, \sqrt{2} {\left(d^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + d^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(i \, a c d + 3 \, a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, a c d - a d^{2}\right)} f\right)} \sqrt{-\frac{4 i \, d^{3}}{a f^{2}}}\right)}}{i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3} + {\left(i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}\right) - a f \sqrt{-\frac{4 i \, d^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{2 \, {\left(4 \, \sqrt{2} {\left(d^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + d^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(-i \, a c d - 3 \, a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, a c d + a d^{2}\right)} f\right)} \sqrt{-\frac{4 i \, d^{3}}{a f^{2}}}\right)}}{i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3} + {\left(i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}\right) + a f \sqrt{-\frac{2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{a f \sqrt{-\frac{2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{i \, c + d}\right) - a f \sqrt{-\frac{2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(-\frac{a f \sqrt{-\frac{2 \, c^{3} - 6 i \, c^{2} d - 6 \, c d^{2} + 2 i \, d^{3}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{i \, c + d}\right) - \sqrt{2} {\left({\left(2 i \, c - 2 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, c - 2 \, d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a f}"," ",0,"-1/4*(a*f*sqrt(-4*I*d^3/(a*f^2))*e^(I*f*x + I*e)*log(2*(4*sqrt(2)*(d^3*e^(3*I*f*x + 3*I*e) + d^3*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((I*a*c*d + 3*a*d^2)*f*e^(2*I*f*x + 2*I*e) + (I*a*c*d - a*d^2)*f)*sqrt(-4*I*d^3/(a*f^2)))/(I*c^3 + c^2*d + I*c*d^2 + d^3 + (I*c^3 + c^2*d + I*c*d^2 + d^3)*e^(2*I*f*x + 2*I*e))) - a*f*sqrt(-4*I*d^3/(a*f^2))*e^(I*f*x + I*e)*log(2*(4*sqrt(2)*(d^3*e^(3*I*f*x + 3*I*e) + d^3*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((-I*a*c*d - 3*a*d^2)*f*e^(2*I*f*x + 2*I*e) + (-I*a*c*d + a*d^2)*f)*sqrt(-4*I*d^3/(a*f^2)))/(I*c^3 + c^2*d + I*c*d^2 + d^3 + (I*c^3 + c^2*d + I*c*d^2 + d^3)*e^(2*I*f*x + 2*I*e))) + a*f*sqrt(-(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)/(a*f^2))*e^(I*f*x + I*e)*log((a*f*sqrt(-(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)/(a*f^2))*e^(I*f*x + I*e) + sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(I*c + d)) - a*f*sqrt(-(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)/(a*f^2))*e^(I*f*x + I*e)*log(-(a*f*sqrt(-(2*c^3 - 6*I*c^2*d - 6*c*d^2 + 2*I*d^3)/(a*f^2))*e^(I*f*x + I*e) - sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(I*c + d)) - sqrt(2)*((2*I*c - 2*d)*e^(2*I*f*x + 2*I*e) + 2*I*c - 2*d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)","B",0
1147,1,489,0,0.504184," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{i \, c + d}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{i \, c + d}\right) - \sqrt{2} {\left({\left(4 i \, c + 4 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(5 i \, c + 3 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{12 \, a^{2} f}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log((2*sqrt(1/2)*a^2*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(I*c + d)) - 3*sqrt(1/2)*a^2*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(-(2*sqrt(1/2)*a^2*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(I*c + d)) - sqrt(2)*((4*I*c + 4*d)*e^(4*I*f*x + 4*I*e) + (5*I*c + 3*d)*e^(2*I*f*x + 2*I*e) + I*c - d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-3*I*f*x - 3*I*e)/(a^2*f)","B",0
1148,1,569,0,0.501400," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} {\left(-i \, a^{3} c + a^{3} d\right)} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{5} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{i \, c + d}\right) + 15 \, \sqrt{\frac{1}{2}} {\left(i \, a^{3} c - a^{3} d\right)} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}}{a^{5} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left({\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{i \, c + d}\right) - \sqrt{2} {\left(3 \, c^{2} + 6 i \, c d - 3 \, d^{2} + {\left(23 \, c^{2} - 6 i \, c d + 17 \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(34 \, c^{2} + 4 i \, c d + 18 \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(14 \, c^{2} + 16 i \, c d - 2 \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{120 \, {\left(i \, a^{3} c - a^{3} d\right)} f}"," ",0,"1/120*(15*sqrt(1/2)*(-I*a^3*c + a^3*d)*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log((2*sqrt(1/2)*a^3*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^5*f^2))*e^(I*f*x + I*e) + sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(I*c + d)) + 15*sqrt(1/2)*(I*a^3*c - a^3*d)*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(-(2*sqrt(1/2)*a^3*f*sqrt(-(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)/(a^5*f^2))*e^(I*f*x + I*e) - sqrt(2)*((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(I*c + d)) - sqrt(2)*(3*c^2 + 6*I*c*d - 3*d^2 + (23*c^2 - 6*I*c*d + 17*d^2)*e^(6*I*f*x + 6*I*e) + (34*c^2 + 4*I*c*d + 18*d^2)*e^(4*I*f*x + 4*I*e) + (14*c^2 + 16*I*c*d - 2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-5*I*f*x - 5*I*e)/((I*a^3*c - a^3*d)*f)","B",0
1149,1,1914,0,0.782820," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} {\left({\left(15 \, a^{2} c^{3} - 719 i \, a^{2} c^{2} d - 1621 \, a^{2} c d^{2} + 845 i \, a^{2} d^{3}\right)} e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(45 \, a^{2} c^{3} - 1921 i \, a^{2} c^{2} d - 3415 \, a^{2} c d^{2} + 1275 i \, a^{2} d^{3}\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(45 \, a^{2} c^{3} - 1685 i \, a^{2} c^{2} d - 2511 \, a^{2} c d^{2} + 1135 i \, a^{2} d^{3}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(15 \, a^{2} c^{3} - 483 i \, a^{2} c^{2} d - 717 \, a^{2} c d^{2} + 321 i \, a^{2} d^{3}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - 3 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{25 i \, a^{5} c^{8} - 1000 \, a^{5} c^{7} d - 3100 i \, a^{5} c^{6} d^{2} - 129000 \, a^{5} c^{5} d^{3} + 652470 i \, a^{5} c^{4} d^{4} + 1314600 \, a^{5} c^{3} d^{5} - 1310940 i \, a^{5} c^{2} d^{6} - 653400 \, a^{5} c d^{7} + 131769 i \, a^{5} d^{8}}{d^{3} f^{2}}} \log\left(-\frac{{\left(2 i \, d^{2} f \sqrt{\frac{25 i \, a^{5} c^{8} - 1000 \, a^{5} c^{7} d - 3100 i \, a^{5} c^{6} d^{2} - 129000 \, a^{5} c^{5} d^{3} + 652470 i \, a^{5} c^{4} d^{4} + 1314600 \, a^{5} c^{3} d^{5} - 1310940 i \, a^{5} c^{2} d^{6} - 653400 \, a^{5} c d^{7} + 131769 i \, a^{5} d^{8}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(5 \, a^{2} c^{4} + 100 i \, a^{2} c^{3} d + 690 \, a^{2} c^{2} d^{2} - 900 i \, a^{2} c d^{3} - 363 \, a^{2} d^{4} + {\left(5 \, a^{2} c^{4} + 100 i \, a^{2} c^{3} d + 690 \, a^{2} c^{2} d^{2} - 900 i \, a^{2} c d^{3} - 363 \, a^{2} d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{5 \, a^{2} c^{4} + 100 i \, a^{2} c^{3} d + 690 \, a^{2} c^{2} d^{2} - 900 i \, a^{2} c d^{3} - 363 \, a^{2} d^{4}}\right) + 3 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{\frac{25 i \, a^{5} c^{8} - 1000 \, a^{5} c^{7} d - 3100 i \, a^{5} c^{6} d^{2} - 129000 \, a^{5} c^{5} d^{3} + 652470 i \, a^{5} c^{4} d^{4} + 1314600 \, a^{5} c^{3} d^{5} - 1310940 i \, a^{5} c^{2} d^{6} - 653400 \, a^{5} c d^{7} + 131769 i \, a^{5} d^{8}}{d^{3} f^{2}}} \log\left(-\frac{{\left(-2 i \, d^{2} f \sqrt{\frac{25 i \, a^{5} c^{8} - 1000 \, a^{5} c^{7} d - 3100 i \, a^{5} c^{6} d^{2} - 129000 \, a^{5} c^{5} d^{3} + 652470 i \, a^{5} c^{4} d^{4} + 1314600 \, a^{5} c^{3} d^{5} - 1310940 i \, a^{5} c^{2} d^{6} - 653400 \, a^{5} c d^{7} + 131769 i \, a^{5} d^{8}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(5 \, a^{2} c^{4} + 100 i \, a^{2} c^{3} d + 690 \, a^{2} c^{2} d^{2} - 900 i \, a^{2} c d^{3} - 363 \, a^{2} d^{4} + {\left(5 \, a^{2} c^{4} + 100 i \, a^{2} c^{3} d + 690 \, a^{2} c^{2} d^{2} - 900 i \, a^{2} c d^{3} - 363 \, a^{2} d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{5 \, a^{2} c^{4} + 100 i \, a^{2} c^{3} d + 690 \, a^{2} c^{2} d^{2} - 900 i \, a^{2} c d^{3} - 363 \, a^{2} d^{4}}\right) - 192 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{32 \, a^{5} c^{5} - 160 i \, a^{5} c^{4} d - 320 \, a^{5} c^{3} d^{2} + 320 i \, a^{5} c^{2} d^{3} + 160 \, a^{5} c d^{4} - 32 i \, a^{5} d^{5}}{f^{2}}} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2} + {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + i \, f \sqrt{-\frac{32 \, a^{5} c^{5} - 160 i \, a^{5} c^{4} d - 320 \, a^{5} c^{3} d^{2} + 320 i \, a^{5} c^{2} d^{3} + 160 \, a^{5} c d^{4} - 32 i \, a^{5} d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)}}\right) + 192 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)} \sqrt{-\frac{32 \, a^{5} c^{5} - 160 i \, a^{5} c^{4} d - 320 \, a^{5} c^{3} d^{2} + 320 i \, a^{5} c^{2} d^{3} + 160 \, a^{5} c d^{4} - 32 i \, a^{5} d^{5}}{f^{2}}} \log\left(\frac{{\left(4 \, \sqrt{2} {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2} + {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - i \, f \sqrt{-\frac{32 \, a^{5} c^{5} - 160 i \, a^{5} c^{4} d - 320 \, a^{5} c^{3} d^{2} + 320 i \, a^{5} c^{2} d^{3} + 160 \, a^{5} c d^{4} - 32 i \, a^{5} d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, {\left(a^{2} c^{2} - 2 i \, a^{2} c d - a^{2} d^{2}\right)}}\right)}{384 \, {\left(d f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, d f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f\right)}}"," ",0,"-1/384*(2*sqrt(2)*((15*a^2*c^3 - 719*I*a^2*c^2*d - 1621*a^2*c*d^2 + 845*I*a^2*d^3)*e^(7*I*f*x + 7*I*e) + (45*a^2*c^3 - 1921*I*a^2*c^2*d - 3415*a^2*c*d^2 + 1275*I*a^2*d^3)*e^(5*I*f*x + 5*I*e) + (45*a^2*c^3 - 1685*I*a^2*c^2*d - 2511*a^2*c*d^2 + 1135*I*a^2*d^3)*e^(3*I*f*x + 3*I*e) + (15*a^2*c^3 - 483*I*a^2*c^2*d - 717*a^2*c*d^2 + 321*I*a^2*d^3)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - 3*(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((25*I*a^5*c^8 - 1000*a^5*c^7*d - 3100*I*a^5*c^6*d^2 - 129000*a^5*c^5*d^3 + 652470*I*a^5*c^4*d^4 + 1314600*a^5*c^3*d^5 - 1310940*I*a^5*c^2*d^6 - 653400*a^5*c*d^7 + 131769*I*a^5*d^8)/(d^3*f^2))*log(-(2*I*d^2*f*sqrt((25*I*a^5*c^8 - 1000*a^5*c^7*d - 3100*I*a^5*c^6*d^2 - 129000*a^5*c^5*d^3 + 652470*I*a^5*c^4*d^4 + 1314600*a^5*c^3*d^5 - 1310940*I*a^5*c^2*d^6 - 653400*a^5*c*d^7 + 131769*I*a^5*d^8)/(d^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*(5*a^2*c^4 + 100*I*a^2*c^3*d + 690*a^2*c^2*d^2 - 900*I*a^2*c*d^3 - 363*a^2*d^4 + (5*a^2*c^4 + 100*I*a^2*c^3*d + 690*a^2*c^2*d^2 - 900*I*a^2*c*d^3 - 363*a^2*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(5*a^2*c^4 + 100*I*a^2*c^3*d + 690*a^2*c^2*d^2 - 900*I*a^2*c*d^3 - 363*a^2*d^4)) + 3*(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt((25*I*a^5*c^8 - 1000*a^5*c^7*d - 3100*I*a^5*c^6*d^2 - 129000*a^5*c^5*d^3 + 652470*I*a^5*c^4*d^4 + 1314600*a^5*c^3*d^5 - 1310940*I*a^5*c^2*d^6 - 653400*a^5*c*d^7 + 131769*I*a^5*d^8)/(d^3*f^2))*log(-(-2*I*d^2*f*sqrt((25*I*a^5*c^8 - 1000*a^5*c^7*d - 3100*I*a^5*c^6*d^2 - 129000*a^5*c^5*d^3 + 652470*I*a^5*c^4*d^4 + 1314600*a^5*c^3*d^5 - 1310940*I*a^5*c^2*d^6 - 653400*a^5*c*d^7 + 131769*I*a^5*d^8)/(d^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*(5*a^2*c^4 + 100*I*a^2*c^3*d + 690*a^2*c^2*d^2 - 900*I*a^2*c*d^3 - 363*a^2*d^4 + (5*a^2*c^4 + 100*I*a^2*c^3*d + 690*a^2*c^2*d^2 - 900*I*a^2*c*d^3 - 363*a^2*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(5*a^2*c^4 + 100*I*a^2*c^3*d + 690*a^2*c^2*d^2 - 900*I*a^2*c*d^3 - 363*a^2*d^4)) - 192*(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(32*a^5*c^5 - 160*I*a^5*c^4*d - 320*a^5*c^3*d^2 + 320*I*a^5*c^2*d^3 + 160*a^5*c*d^4 - 32*I*a^5*d^5)/f^2)*log(1/4*(4*sqrt(2)*(a^2*c^2 - 2*I*a^2*c*d - a^2*d^2 + (a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + I*f*sqrt(-(32*a^5*c^5 - 160*I*a^5*c^4*d - 320*a^5*c^3*d^2 + 320*I*a^5*c^2*d^3 + 160*a^5*c*d^4 - 32*I*a^5*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)) + 192*(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)*sqrt(-(32*a^5*c^5 - 160*I*a^5*c^4*d - 320*a^5*c^3*d^2 + 320*I*a^5*c^2*d^3 + 160*a^5*c*d^4 - 32*I*a^5*d^5)/f^2)*log(1/4*(4*sqrt(2)*(a^2*c^2 - 2*I*a^2*c*d - a^2*d^2 + (a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - I*f*sqrt(-(32*a^5*c^5 - 160*I*a^5*c^4*d - 320*a^5*c^3*d^2 + 320*I*a^5*c^2*d^3 + 160*a^5*c*d^4 - 32*I*a^5*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(a^2*c^2 - 2*I*a^2*c*d - a^2*d^2)))/(d*f*e^(6*I*f*x + 6*I*e) + 3*d*f*e^(4*I*f*x + 4*I*e) + 3*d*f*e^(2*I*f*x + 2*I*e) + d*f)","B",0
1150,1,1487,0,0.674937," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left({\left(33 i \, a c^{2} + 94 \, a c d - 49 i \, a d^{2}\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(66 i \, a c^{2} + 136 \, a c d - 38 i \, a d^{2}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(33 i \, a c^{2} + 42 \, a c d - 21 i \, a d^{2}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + 3 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-25 i \, a^{3} c^{6} - 450 \, a^{3} c^{5} d + 2575 i \, a^{3} c^{4} d^{2} + 5180 \, a^{3} c^{3} d^{3} - 5095 i \, a^{3} c^{2} d^{4} - 2530 \, a^{3} c d^{5} + 529 i \, a^{3} d^{6}}{d f^{2}}} \log\left(\frac{{\left(2 i \, d f \sqrt{\frac{-25 i \, a^{3} c^{6} - 450 \, a^{3} c^{5} d + 2575 i \, a^{3} c^{4} d^{2} + 5180 \, a^{3} c^{3} d^{3} - 5095 i \, a^{3} c^{2} d^{4} - 2530 \, a^{3} c d^{5} + 529 i \, a^{3} d^{6}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(-5 i \, a c^{3} - 45 \, a c^{2} d + 55 i \, a c d^{2} + 23 \, a d^{3} + {\left(-5 i \, a c^{3} - 45 \, a c^{2} d + 55 i \, a c d^{2} + 23 \, a d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{-5 i \, a c^{3} - 45 \, a c^{2} d + 55 i \, a c d^{2} + 23 \, a d^{3}}\right) - 3 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{-25 i \, a^{3} c^{6} - 450 \, a^{3} c^{5} d + 2575 i \, a^{3} c^{4} d^{2} + 5180 \, a^{3} c^{3} d^{3} - 5095 i \, a^{3} c^{2} d^{4} - 2530 \, a^{3} c d^{5} + 529 i \, a^{3} d^{6}}{d f^{2}}} \log\left(\frac{{\left(-2 i \, d f \sqrt{\frac{-25 i \, a^{3} c^{6} - 450 \, a^{3} c^{5} d + 2575 i \, a^{3} c^{4} d^{2} + 5180 \, a^{3} c^{3} d^{3} - 5095 i \, a^{3} c^{2} d^{4} - 2530 \, a^{3} c d^{5} + 529 i \, a^{3} d^{6}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(-5 i \, a c^{3} - 45 \, a c^{2} d + 55 i \, a c d^{2} + 23 \, a d^{3} + {\left(-5 i \, a c^{3} - 45 \, a c^{2} d + 55 i \, a c d^{2} + 23 \, a d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{-5 i \, a c^{3} - 45 \, a c^{2} d + 55 i \, a c d^{2} + 23 \, a d^{3}}\right) + 24 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{8 \, a^{3} c^{5} - 40 i \, a^{3} c^{4} d - 80 \, a^{3} c^{3} d^{2} + 80 i \, a^{3} c^{2} d^{3} + 40 \, a^{3} c d^{4} - 8 i \, a^{3} d^{5}}{f^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a c^{2} - 2 i \, a c d - a d^{2} + {\left(a c^{2} - 2 i \, a c d - a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + i \, f \sqrt{-\frac{8 \, a^{3} c^{5} - 40 i \, a^{3} c^{4} d - 80 \, a^{3} c^{3} d^{2} + 80 i \, a^{3} c^{2} d^{3} + 40 \, a^{3} c d^{4} - 8 i \, a^{3} d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, {\left(a c^{2} - 2 i \, a c d - a d^{2}\right)}}\right) - 24 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{8 \, a^{3} c^{5} - 40 i \, a^{3} c^{4} d - 80 \, a^{3} c^{3} d^{2} + 80 i \, a^{3} c^{2} d^{3} + 40 \, a^{3} c d^{4} - 8 i \, a^{3} d^{5}}{f^{2}}} \log\left(\frac{{\left(2 \, \sqrt{2} {\left(a c^{2} - 2 i \, a c d - a d^{2} + {\left(a c^{2} - 2 i \, a c d - a d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - i \, f \sqrt{-\frac{8 \, a^{3} c^{5} - 40 i \, a^{3} c^{4} d - 80 \, a^{3} c^{3} d^{2} + 80 i \, a^{3} c^{2} d^{3} + 40 \, a^{3} c d^{4} - 8 i \, a^{3} d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, {\left(a c^{2} - 2 i \, a c d - a d^{2}\right)}}\right)}{48 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/48*(2*sqrt(2)*((33*I*a*c^2 + 94*a*c*d - 49*I*a*d^2)*e^(5*I*f*x + 5*I*e) + (66*I*a*c^2 + 136*a*c*d - 38*I*a*d^2)*e^(3*I*f*x + 3*I*e) + (33*I*a*c^2 + 42*a*c*d - 21*I*a*d^2)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + 3*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-25*I*a^3*c^6 - 450*a^3*c^5*d + 2575*I*a^3*c^4*d^2 + 5180*a^3*c^3*d^3 - 5095*I*a^3*c^2*d^4 - 2530*a^3*c*d^5 + 529*I*a^3*d^6)/(d*f^2))*log((2*I*d*f*sqrt((-25*I*a^3*c^6 - 450*a^3*c^5*d + 2575*I*a^3*c^4*d^2 + 5180*a^3*c^3*d^3 - 5095*I*a^3*c^2*d^4 - 2530*a^3*c*d^5 + 529*I*a^3*d^6)/(d*f^2))*e^(I*f*x + I*e) + sqrt(2)*(-5*I*a*c^3 - 45*a*c^2*d + 55*I*a*c*d^2 + 23*a*d^3 + (-5*I*a*c^3 - 45*a*c^2*d + 55*I*a*c*d^2 + 23*a*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(-5*I*a*c^3 - 45*a*c^2*d + 55*I*a*c*d^2 + 23*a*d^3)) - 3*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*sqrt((-25*I*a^3*c^6 - 450*a^3*c^5*d + 2575*I*a^3*c^4*d^2 + 5180*a^3*c^3*d^3 - 5095*I*a^3*c^2*d^4 - 2530*a^3*c*d^5 + 529*I*a^3*d^6)/(d*f^2))*log((-2*I*d*f*sqrt((-25*I*a^3*c^6 - 450*a^3*c^5*d + 2575*I*a^3*c^4*d^2 + 5180*a^3*c^3*d^3 - 5095*I*a^3*c^2*d^4 - 2530*a^3*c*d^5 + 529*I*a^3*d^6)/(d*f^2))*e^(I*f*x + I*e) + sqrt(2)*(-5*I*a*c^3 - 45*a*c^2*d + 55*I*a*c*d^2 + 23*a*d^3 + (-5*I*a*c^3 - 45*a*c^2*d + 55*I*a*c*d^2 + 23*a*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(-5*I*a*c^3 - 45*a*c^2*d + 55*I*a*c*d^2 + 23*a*d^3)) + 24*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(8*a^3*c^5 - 40*I*a^3*c^4*d - 80*a^3*c^3*d^2 + 80*I*a^3*c^2*d^3 + 40*a^3*c*d^4 - 8*I*a^3*d^5)/f^2)*log(1/2*(2*sqrt(2)*(a*c^2 - 2*I*a*c*d - a*d^2 + (a*c^2 - 2*I*a*c*d - a*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + I*f*sqrt(-(8*a^3*c^5 - 40*I*a^3*c^4*d - 80*a^3*c^3*d^2 + 80*I*a^3*c^2*d^3 + 40*a^3*c*d^4 - 8*I*a^3*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(a*c^2 - 2*I*a*c*d - a*d^2)) - 24*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(8*a^3*c^5 - 40*I*a^3*c^4*d - 80*a^3*c^3*d^2 + 80*I*a^3*c^2*d^3 + 40*a^3*c*d^4 - 8*I*a^3*d^5)/f^2)*log(1/2*(2*sqrt(2)*(a*c^2 - 2*I*a*c*d - a*d^2 + (a*c^2 - 2*I*a*c*d - a*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - I*f*sqrt(-(8*a^3*c^5 - 40*I*a^3*c^4*d - 80*a^3*c^3*d^2 + 80*I*a^3*c^2*d^3 + 40*a^3*c*d^4 - 8*I*a^3*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(a*c^2 - 2*I*a*c*d - a*d^2)))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1151,1,1105,0,0.643239," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(3 \, {\left(3 \, c d - i \, d^{2}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(9 \, c d + i \, d^{2}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{225 i \, a c^{4} d + 300 \, a c^{3} d^{2} - 310 i \, a c^{2} d^{3} - 140 \, a c d^{4} + 49 i \, a d^{5}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(15 \, c^{2} - 10 i \, c d - 7 \, d^{2} + {\left(15 \, c^{2} - 10 i \, c d - 7 \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + 2 i \, f \sqrt{\frac{225 i \, a c^{4} d + 300 \, a c^{3} d^{2} - 310 i \, a c^{2} d^{3} - 140 \, a c d^{4} + 49 i \, a d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{15 \, c^{2} - 10 i \, c d - 7 \, d^{2}}\right) + {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{\frac{225 i \, a c^{4} d + 300 \, a c^{3} d^{2} - 310 i \, a c^{2} d^{3} - 140 \, a c d^{4} + 49 i \, a d^{5}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(15 \, c^{2} - 10 i \, c d - 7 \, d^{2} + {\left(15 \, c^{2} - 10 i \, c d - 7 \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - 2 i \, f \sqrt{\frac{225 i \, a c^{4} d + 300 \, a c^{3} d^{2} - 310 i \, a c^{2} d^{3} - 140 \, a c d^{4} + 49 i \, a d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{15 \, c^{2} - 10 i \, c d - 7 \, d^{2}}\right) + 4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{2 \, a c^{5} - 10 i \, a c^{4} d - 20 \, a c^{3} d^{2} + 20 i \, a c^{2} d^{3} + 10 \, a c d^{4} - 2 i \, a d^{5}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + i \, f \sqrt{-\frac{2 \, a c^{5} - 10 i \, a c^{4} d - 20 \, a c^{3} d^{2} + 20 i \, a c^{2} d^{3} + 10 \, a c d^{4} - 2 i \, a d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{c^{2} - 2 i \, c d - d^{2}}\right) - 4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} \sqrt{-\frac{2 \, a c^{5} - 10 i \, a c^{4} d - 20 \, a c^{3} d^{2} + 20 i \, a c^{2} d^{3} + 10 \, a c d^{4} - 2 i \, a d^{5}}{f^{2}}} \log\left(\frac{{\left(\sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - i \, f \sqrt{-\frac{2 \, a c^{5} - 10 i \, a c^{4} d - 20 \, a c^{3} d^{2} + 20 i \, a c^{2} d^{3} + 10 \, a c d^{4} - 2 i \, a d^{5}}{f^{2}}} e^{\left(i \, f x + i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{c^{2} - 2 i \, c d - d^{2}}\right)}{8 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/8*(2*sqrt(2)*(3*(3*c*d - I*d^2)*e^(3*I*f*x + 3*I*e) + (9*c*d + I*d^2)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - (f*e^(2*I*f*x + 2*I*e) + f)*sqrt((225*I*a*c^4*d + 300*a*c^3*d^2 - 310*I*a*c^2*d^3 - 140*a*c*d^4 + 49*I*a*d^5)/f^2)*log((sqrt(2)*(15*c^2 - 10*I*c*d - 7*d^2 + (15*c^2 - 10*I*c*d - 7*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + 2*I*f*sqrt((225*I*a*c^4*d + 300*a*c^3*d^2 - 310*I*a*c^2*d^3 - 140*a*c*d^4 + 49*I*a*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(15*c^2 - 10*I*c*d - 7*d^2)) + (f*e^(2*I*f*x + 2*I*e) + f)*sqrt((225*I*a*c^4*d + 300*a*c^3*d^2 - 310*I*a*c^2*d^3 - 140*a*c*d^4 + 49*I*a*d^5)/f^2)*log((sqrt(2)*(15*c^2 - 10*I*c*d - 7*d^2 + (15*c^2 - 10*I*c*d - 7*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - 2*I*f*sqrt((225*I*a*c^4*d + 300*a*c^3*d^2 - 310*I*a*c^2*d^3 - 140*a*c*d^4 + 49*I*a*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(15*c^2 - 10*I*c*d - 7*d^2)) + 4*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(2*a*c^5 - 10*I*a*c^4*d - 20*a*c^3*d^2 + 20*I*a*c^2*d^3 + 10*a*c*d^4 - 2*I*a*d^5)/f^2)*log((sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + I*f*sqrt(-(2*a*c^5 - 10*I*a*c^4*d - 20*a*c^3*d^2 + 20*I*a*c^2*d^3 + 10*a*c*d^4 - 2*I*a*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(c^2 - 2*I*c*d - d^2)) - 4*(f*e^(2*I*f*x + 2*I*e) + f)*sqrt(-(2*a*c^5 - 10*I*a*c^4*d - 20*a*c^3*d^2 + 20*I*a*c^2*d^3 + 10*a*c*d^4 - 2*I*a*d^5)/f^2)*log((sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - I*f*sqrt(-(2*a*c^5 - 10*I*a*c^4*d - 20*a*c^3*d^2 + 20*I*a*c^2*d^3 + 10*a*c*d^4 - 2*I*a*d^5)/f^2)*e^(I*f*x + I*e))*e^(-I*f*x - I*e)/(c^2 - 2*I*c*d - d^2)))/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
1152,1,1158,0,1.082367," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a f \sqrt{\frac{-25 i \, c^{2} d^{3} + 10 \, c d^{4} + i \, d^{5}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{\sqrt{2} {\left({\left(-40 i \, c d^{3} + 8 \, d^{4}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-40 i \, c d^{3} + 8 \, d^{4}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(4 \, a c d - 12 i \, a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 \, a c d + 4 i \, a d^{2}\right)} f\right)} \sqrt{\frac{-25 i \, c^{2} d^{3} + 10 \, c d^{4} + i \, d^{5}}{a f^{2}}}}{5 \, c^{4} - 4 i \, c^{3} d + 6 \, c^{2} d^{2} - 4 i \, c d^{3} + d^{4} + {\left(5 \, c^{4} - 4 i \, c^{3} d + 6 \, c^{2} d^{2} - 4 i \, c d^{3} + d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}\right) - a f \sqrt{\frac{-25 i \, c^{2} d^{3} + 10 \, c d^{4} + i \, d^{5}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(\frac{\sqrt{2} {\left({\left(-40 i \, c d^{3} + 8 \, d^{4}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-40 i \, c d^{3} + 8 \, d^{4}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(4 \, a c d - 12 i \, a d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(4 \, a c d + 4 i \, a d^{2}\right)} f\right)} \sqrt{\frac{-25 i \, c^{2} d^{3} + 10 \, c d^{4} + i \, d^{5}}{a f^{2}}}}{5 \, c^{4} - 4 i \, c^{3} d + 6 \, c^{2} d^{2} - 4 i \, c d^{3} + d^{4} + {\left(5 \, c^{4} - 4 i \, c^{3} d + 6 \, c^{2} d^{2} - 4 i \, c d^{3} + d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}\right) - a f \sqrt{-\frac{2 \, c^{5} - 10 i \, c^{4} d - 20 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} + 10 \, c d^{4} - 2 i \, d^{5}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(-\frac{i \, a f \sqrt{-\frac{2 \, c^{5} - 10 i \, c^{4} d - 20 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} + 10 \, c d^{4} - 2 i \, d^{5}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c^{2} - 2 i \, c d - d^{2}}\right) + a f \sqrt{-\frac{2 \, c^{5} - 10 i \, c^{4} d - 20 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} + 10 \, c d^{4} - 2 i \, d^{5}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left(-\frac{-i \, a f \sqrt{-\frac{2 \, c^{5} - 10 i \, c^{4} d - 20 \, c^{3} d^{2} + 20 i \, c^{2} d^{3} + 10 \, c d^{4} - 2 i \, d^{5}}{a f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c^{2} - 2 i \, c d - d^{2}}\right) + \sqrt{2} {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 6 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a f}"," ",0,"1/4*(a*f*sqrt((-25*I*c^2*d^3 + 10*c*d^4 + I*d^5)/(a*f^2))*e^(I*f*x + I*e)*log((sqrt(2)*((-40*I*c*d^3 + 8*d^4)*e^(3*I*f*x + 3*I*e) + (-40*I*c*d^3 + 8*d^4)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((4*a*c*d - 12*I*a*d^2)*f*e^(2*I*f*x + 2*I*e) + (4*a*c*d + 4*I*a*d^2)*f)*sqrt((-25*I*c^2*d^3 + 10*c*d^4 + I*d^5)/(a*f^2)))/(5*c^4 - 4*I*c^3*d + 6*c^2*d^2 - 4*I*c*d^3 + d^4 + (5*c^4 - 4*I*c^3*d + 6*c^2*d^2 - 4*I*c*d^3 + d^4)*e^(2*I*f*x + 2*I*e))) - a*f*sqrt((-25*I*c^2*d^3 + 10*c*d^4 + I*d^5)/(a*f^2))*e^(I*f*x + I*e)*log((sqrt(2)*((-40*I*c*d^3 + 8*d^4)*e^(3*I*f*x + 3*I*e) + (-40*I*c*d^3 + 8*d^4)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((4*a*c*d - 12*I*a*d^2)*f*e^(2*I*f*x + 2*I*e) + (4*a*c*d + 4*I*a*d^2)*f)*sqrt((-25*I*c^2*d^3 + 10*c*d^4 + I*d^5)/(a*f^2)))/(5*c^4 - 4*I*c^3*d + 6*c^2*d^2 - 4*I*c*d^3 + d^4 + (5*c^4 - 4*I*c^3*d + 6*c^2*d^2 - 4*I*c*d^3 + d^4)*e^(2*I*f*x + 2*I*e))) - a*f*sqrt(-(2*c^5 - 10*I*c^4*d - 20*c^3*d^2 + 20*I*c^2*d^3 + 10*c*d^4 - 2*I*d^5)/(a*f^2))*e^(I*f*x + I*e)*log(-(I*a*f*sqrt(-(2*c^5 - 10*I*c^4*d - 20*c^3*d^2 + 20*I*c^2*d^3 + 10*c*d^4 - 2*I*d^5)/(a*f^2))*e^(I*f*x + I*e) - sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2 - 2*I*c*d - d^2)) + a*f*sqrt(-(2*c^5 - 10*I*c^4*d - 20*c^3*d^2 + 20*I*c^2*d^3 + 10*c*d^4 - 2*I*d^5)/(a*f^2))*e^(I*f*x + I*e)*log(-(-I*a*f*sqrt(-(2*c^5 - 10*I*c^4*d - 20*c^3*d^2 + 20*I*c^2*d^3 + 10*c*d^4 - 2*I*d^5)/(a*f^2))*e^(I*f*x + I*e) - sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2 - 2*I*c*d - d^2)) + sqrt(2)*(2*I*c^2 - 4*c*d - 2*I*d^2 + (2*I*c^2 - 4*c*d - 6*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(a*f)","B",0
1153,1,1072,0,0.681616," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-\frac{2 i \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c^{2} - 2 i \, c d - d^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-\frac{-2 i \, \sqrt{\frac{1}{2}} a^{2} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c^{2} - 2 i \, c d - d^{2}}\right) + 3 \, a^{2} f \sqrt{\frac{4 i \, d^{5}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{8 \, \sqrt{2} {\left(d^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + d^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(2 \, a^{2} c - 6 i \, a^{2} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 \, a^{2} c + 2 i \, a^{2} d\right)} f\right)} \sqrt{\frac{4 i \, d^{5}}{a^{3} f^{2}}}}{i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3} + {\left(i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}\right) - 3 \, a^{2} f \sqrt{\frac{4 i \, d^{5}}{a^{3} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(\frac{8 \, \sqrt{2} {\left(d^{3} e^{\left(3 i \, f x + 3 i \, e\right)} + d^{3} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(2 \, a^{2} c - 6 i \, a^{2} d\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 \, a^{2} c + 2 i \, a^{2} d\right)} f\right)} \sqrt{\frac{4 i \, d^{5}}{a^{3} f^{2}}}}{i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3} + {\left(i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}\right) - \sqrt{2} {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + {\left(4 i \, c^{2} + 6 \, c d + 10 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(5 i \, c^{2} + 4 \, c d + 9 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{12 \, a^{2} f}"," ",0,"-1/12*(3*sqrt(1/2)*a^2*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(-(2*I*sqrt(1/2)*a^2*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2 - 2*I*c*d - d^2)) - 3*sqrt(1/2)*a^2*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log(-(-2*I*sqrt(1/2)*a^2*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2 - 2*I*c*d - d^2)) + 3*a^2*f*sqrt(4*I*d^5/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log((8*sqrt(2)*(d^3*e^(3*I*f*x + 3*I*e) + d^3*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((2*a^2*c - 6*I*a^2*d)*f*e^(2*I*f*x + 2*I*e) + (2*a^2*c + 2*I*a^2*d)*f)*sqrt(4*I*d^5/(a^3*f^2)))/(I*c^3 + c^2*d + I*c*d^2 + d^3 + (I*c^3 + c^2*d + I*c*d^2 + d^3)*e^(2*I*f*x + 2*I*e))) - 3*a^2*f*sqrt(4*I*d^5/(a^3*f^2))*e^(3*I*f*x + 3*I*e)*log((8*sqrt(2)*(d^3*e^(3*I*f*x + 3*I*e) + d^3*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((2*a^2*c - 6*I*a^2*d)*f*e^(2*I*f*x + 2*I*e) + (2*a^2*c + 2*I*a^2*d)*f)*sqrt(4*I*d^5/(a^3*f^2)))/(I*c^3 + c^2*d + I*c*d^2 + d^3 + (I*c^3 + c^2*d + I*c*d^2 + d^3)*e^(2*I*f*x + 2*I*e))) - sqrt(2)*(I*c^2 - 2*c*d - I*d^2 + (4*I*c^2 + 6*c*d + 10*I*d^2)*e^(4*I*f*x + 4*I*e) + (5*I*c^2 + 4*c*d + 9*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-3*I*f*x - 3*I*e)/(a^2*f)","B",0
1154,1,652,0,0.539140," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(-\frac{2 i \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{5} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c^{2} - 2 i \, c d - d^{2}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{5} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(-\frac{-2 i \, \sqrt{\frac{1}{2}} a^{3} f \sqrt{-\frac{c^{5} - 5 i \, c^{4} d - 10 \, c^{3} d^{2} + 10 i \, c^{2} d^{3} + 5 \, c d^{4} - i \, d^{5}}{a^{5} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{c^{2} - 2 i \, c d - d^{2}}\right) - \sqrt{2} {\left(3 i \, c^{2} - 6 \, c d - 3 i \, d^{2} + {\left(23 i \, c^{2} + 46 \, c d - 23 i \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(34 i \, c^{2} + 46 \, c d - 12 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(14 i \, c^{2} - 6 \, c d + 8 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{120 \, a^{3} f}"," ",0,"-1/120*(15*sqrt(1/2)*a^3*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(-(2*I*sqrt(1/2)*a^3*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^5*f^2))*e^(I*f*x + I*e) - sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2 - 2*I*c*d - d^2)) - 15*sqrt(1/2)*a^3*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^5*f^2))*e^(5*I*f*x + 5*I*e)*log(-(-2*I*sqrt(1/2)*a^3*f*sqrt(-(c^5 - 5*I*c^4*d - 10*c^3*d^2 + 10*I*c^2*d^3 + 5*c*d^4 - I*d^5)/(a^5*f^2))*e^(I*f*x + I*e) - sqrt(2)*(c^2 - 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))/(c^2 - 2*I*c*d - d^2)) - sqrt(2)*(3*I*c^2 - 6*c*d - 3*I*d^2 + (23*I*c^2 + 46*c*d - 23*I*d^2)*e^(6*I*f*x + 6*I*e) + (34*I*c^2 + 46*c*d - 12*I*d^2)*e^(4*I*f*x + 4*I*e) + (14*I*c^2 - 6*c*d + 8*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-5*I*f*x - 5*I*e)/(a^3*f)","B",0
1155,1,781,0,0.546397," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} a^{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} e^{\left(i \, f x + i \, e\right)} + d f \sqrt{\frac{i \, a^{5} c^{2} - 10 \, a^{5} c d - 25 i \, a^{5} d^{2}}{d^{3} f^{2}}} \log\left(\frac{{\left(2 \, d^{2} f \sqrt{\frac{i \, a^{5} c^{2} - 10 \, a^{5} c d - 25 i \, a^{5} d^{2}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(-i \, a^{2} c + 5 \, a^{2} d + {\left(-i \, a^{2} c + 5 \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{-i \, a^{2} c + 5 \, a^{2} d}\right) - d f \sqrt{\frac{i \, a^{5} c^{2} - 10 \, a^{5} c d - 25 i \, a^{5} d^{2}}{d^{3} f^{2}}} \log\left(-\frac{{\left(2 \, d^{2} f \sqrt{\frac{i \, a^{5} c^{2} - 10 \, a^{5} c d - 25 i \, a^{5} d^{2}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(-i \, a^{2} c + 5 \, a^{2} d + {\left(-i \, a^{2} c + 5 \, a^{2} d\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{-i \, a^{2} c + 5 \, a^{2} d}\right) - \sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c + d\right)} f^{2}}} d f \log\left(\frac{{\left(\sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c + d\right)} f^{2}}} {\left(i \, c + d\right)} f e^{\left(i \, f x + i \, e\right)} + 4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right) + \sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c + d\right)} f^{2}}} d f \log\left(\frac{{\left(\sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c + d\right)} f^{2}}} {\left(-i \, c - d\right)} f e^{\left(i \, f x + i \, e\right)} + 4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right)}{2 \, d f}"," ",0,"-1/2*(2*sqrt(2)*a^2*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*e^(I*f*x + I*e) + d*f*sqrt((I*a^5*c^2 - 10*a^5*c*d - 25*I*a^5*d^2)/(d^3*f^2))*log((2*d^2*f*sqrt((I*a^5*c^2 - 10*a^5*c*d - 25*I*a^5*d^2)/(d^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*(-I*a^2*c + 5*a^2*d + (-I*a^2*c + 5*a^2*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(-I*a^2*c + 5*a^2*d)) - d*f*sqrt((I*a^5*c^2 - 10*a^5*c*d - 25*I*a^5*d^2)/(d^3*f^2))*log(-(2*d^2*f*sqrt((I*a^5*c^2 - 10*a^5*c*d - 25*I*a^5*d^2)/(d^3*f^2))*e^(I*f*x + I*e) - sqrt(2)*(-I*a^2*c + 5*a^2*d + (-I*a^2*c + 5*a^2*d)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/(-I*a^2*c + 5*a^2*d)) - sqrt(-32*I*a^5/((I*c + d)*f^2))*d*f*log(1/4*(sqrt(-32*I*a^5/((I*c + d)*f^2))*(I*c + d)*f*e^(I*f*x + I*e) + 4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2) + sqrt(-32*I*a^5/((I*c + d)*f^2))*d*f*log(1/4*(sqrt(-32*I*a^5/((I*c + d)*f^2))*(-I*c - d)*f*e^(I*f*x + I*e) + 4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2))/(d*f)","B",0
1156,1,533,0,0.491259," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c + d\right)} f^{2}}} \log\left(\frac{{\left({\left(i \, c + d\right)} f \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c + d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + 2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right) - \frac{1}{2} \, \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c + d\right)} f^{2}}} \log\left(\frac{{\left({\left(-i \, c - d\right)} f \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c + d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + 2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right) - \frac{1}{2} \, \sqrt{-\frac{4 i \, a^{3}}{d f^{2}}} \log\left(\frac{{\left(d f \sqrt{-\frac{4 i \, a^{3}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i \, a^{3}}{d f^{2}}} \log\left(-\frac{{\left(d f \sqrt{-\frac{4 i \, a^{3}}{d f^{2}}} e^{\left(i \, f x + i \, e\right)} - \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a}\right)"," ",0,"1/2*sqrt(-8*I*a^3/((I*c + d)*f^2))*log(1/2*((I*c + d)*f*sqrt(-8*I*a^3/((I*c + d)*f^2))*e^(I*f*x + I*e) + 2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a) - 1/2*sqrt(-8*I*a^3/((I*c + d)*f^2))*log(1/2*((-I*c - d)*f*sqrt(-8*I*a^3/((I*c + d)*f^2))*e^(I*f*x + I*e) + 2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a) - 1/2*sqrt(-4*I*a^3/(d*f^2))*log((d*f*sqrt(-4*I*a^3/(d*f^2))*e^(I*f*x + I*e) + sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a) + 1/2*sqrt(-4*I*a^3/(d*f^2))*log(-(d*f*sqrt(-4*I*a^3/(d*f^2))*e^(I*f*x + I*e) - sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a)","B",0
1157,1,259,0,0.477078," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{2 i \, a}{{\left(i \, c + d\right)} f^{2}}} \log\left({\left({\left(i \, c + d\right)} f \sqrt{-\frac{2 i \, a}{{\left(i \, c + d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right) - \frac{1}{2} \, \sqrt{-\frac{2 i \, a}{{\left(i \, c + d\right)} f^{2}}} \log\left({\left({\left(-i \, c - d\right)} f \sqrt{-\frac{2 i \, a}{{\left(i \, c + d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right)"," ",0,"1/2*sqrt(-2*I*a/((I*c + d)*f^2))*log(((I*c + d)*f*sqrt(-2*I*a/((I*c + d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e)) - 1/2*sqrt(-2*I*a/((I*c + d)*f^2))*log(((-I*c - d)*f*sqrt(-2*I*a/((I*c + d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e))","B",0
1158,1,381,0,0.517021," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(-i \, a c + a d\right)} f \sqrt{-\frac{2 i}{{\left(i \, a c + a d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left({\left(i \, a c + a d\right)} f \sqrt{-\frac{2 i}{{\left(i \, a c + a d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + {\left(i \, a c - a d\right)} f \sqrt{-\frac{2 i}{{\left(i \, a c + a d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} \log\left({\left(-i \, a c - a d\right)} f \sqrt{-\frac{2 i}{{\left(i \, a c + a d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + 2 \, \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, {\left(i \, a c - a d\right)} f}"," ",0,"-1/4*((-I*a*c + a*d)*f*sqrt(-2*I/((I*a*c + a*d)*f^2))*e^(I*f*x + I*e)*log((I*a*c + a*d)*f*sqrt(-2*I/((I*a*c + a*d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + (I*a*c - a*d)*f*sqrt(-2*I/((I*a*c + a*d)*f^2))*e^(I*f*x + I*e)*log((-I*a*c - a*d)*f*sqrt(-2*I/((I*a*c + a*d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + 2*sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e)/((I*a*c - a*d)*f)","B",0
1159,1,483,0,0.515181," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f \sqrt{\frac{i}{2 \, {\left(-i \, a^{3} c - a^{3} d\right)} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-2 \, {\left(i \, a^{2} c + a^{2} d\right)} f \sqrt{\frac{i}{2 \, {\left(-i \, a^{3} c - a^{3} d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - 3 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f \sqrt{\frac{i}{2 \, {\left(-i \, a^{3} c - a^{3} d\right)} f^{2}}} e^{\left(3 i \, f x + 3 i \, e\right)} \log\left(-2 \, {\left(-i \, a^{2} c - a^{2} d\right)} f \sqrt{\frac{i}{2 \, {\left(-i \, a^{3} c - a^{3} d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + \sqrt{2} {\left({\left(-4 i \, c + 8 \, d\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-5 i \, c + 9 \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - i \, c + d\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{12 \, {\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} f}"," ",0,"-1/12*(3*(a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*sqrt(1/2*I/((-I*a^3*c - a^3*d)*f^2))*e^(3*I*f*x + 3*I*e)*log(-2*(I*a^2*c + a^2*d)*f*sqrt(1/2*I/((-I*a^3*c - a^3*d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - 3*(a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f*sqrt(1/2*I/((-I*a^3*c - a^3*d)*f^2))*e^(3*I*f*x + 3*I*e)*log(-2*(-I*a^2*c - a^2*d)*f*sqrt(1/2*I/((-I*a^3*c - a^3*d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + sqrt(2)*((-4*I*c + 8*d)*e^(4*I*f*x + 4*I*e) + (-5*I*c + 9*d)*e^(2*I*f*x + 2*I*e) - I*c + d)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-3*I*f*x - 3*I*e)/((a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*f)","B",0
1160,1,568,0,0.556374," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(-30 i \, a^{3} c^{3} + 90 \, a^{3} c^{2} d + 90 i \, a^{3} c d^{2} - 30 \, a^{3} d^{3}\right)} f \sqrt{\frac{i}{8 \, {\left(-i \, a^{5} c - a^{5} d\right)} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(-4 \, {\left(i \, a^{3} c + a^{3} d\right)} f \sqrt{\frac{i}{8 \, {\left(-i \, a^{5} c - a^{5} d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + {\left(30 i \, a^{3} c^{3} - 90 \, a^{3} c^{2} d - 90 i \, a^{3} c d^{2} + 30 \, a^{3} d^{3}\right)} f \sqrt{\frac{i}{8 \, {\left(-i \, a^{5} c - a^{5} d\right)} f^{2}}} e^{\left(5 i \, f x + 5 i \, e\right)} \log\left(-4 \, {\left(-i \, a^{3} c - a^{3} d\right)} f \sqrt{\frac{i}{8 \, {\left(-i \, a^{5} c - a^{5} d\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - \sqrt{2} {\left(3 \, c^{2} + 6 i \, c d - 3 \, d^{2} + {\left(23 \, c^{2} + 74 i \, c d - 83 \, d^{2}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(34 \, c^{2} + 104 i \, c d - 102 \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(14 \, c^{2} + 36 i \, c d - 22 \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-5 i \, f x - 5 i \, e\right)}}{{\left(120 i \, a^{3} c^{3} - 360 \, a^{3} c^{2} d - 360 i \, a^{3} c d^{2} + 120 \, a^{3} d^{3}\right)} f}"," ",0,"((-30*I*a^3*c^3 + 90*a^3*c^2*d + 90*I*a^3*c*d^2 - 30*a^3*d^3)*f*sqrt(1/8*I/((-I*a^5*c - a^5*d)*f^2))*e^(5*I*f*x + 5*I*e)*log(-4*(I*a^3*c + a^3*d)*f*sqrt(1/8*I/((-I*a^5*c - a^5*d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + (30*I*a^3*c^3 - 90*a^3*c^2*d - 90*I*a^3*c*d^2 + 30*a^3*d^3)*f*sqrt(1/8*I/((-I*a^5*c - a^5*d)*f^2))*e^(5*I*f*x + 5*I*e)*log(-4*(-I*a^3*c - a^3*d)*f*sqrt(1/8*I/((-I*a^5*c - a^5*d)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - sqrt(2)*(3*c^2 + 6*I*c*d - 3*d^2 + (23*c^2 + 74*I*c*d - 83*d^2)*e^(6*I*f*x + 6*I*e) + (34*c^2 + 104*I*c*d - 102*d^2)*e^(4*I*f*x + 4*I*e) + (14*c^2 + 36*I*c*d - 22*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-5*I*f*x - 5*I*e)/((120*I*a^3*c^3 - 360*a^3*c^2*d - 360*I*a^3*c*d^2 + 120*a^3*d^3)*f)","B",0
1161,1,942,0,0.522486," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(4 \, a^{2} c + 4 i \, a^{2} d\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 \, a^{2} c + 4 i \, a^{2} d\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(c^{2} d - 2 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d + d^{3}\right)} f\right)} \sqrt{\frac{4 i \, a^{5}}{d^{3} f^{2}}} \log\left(\frac{{\left(i \, d^{2} f \sqrt{\frac{4 i \, a^{5}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a^{2}}\right) - {\left({\left(c^{2} d - 2 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d + d^{3}\right)} f\right)} \sqrt{\frac{4 i \, a^{5}}{d^{3} f^{2}}} \log\left(\frac{{\left(-i \, d^{2} f \sqrt{\frac{4 i \, a^{5}}{d^{3} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{a^{2}}\right) + {\left({\left(c^{2} d - 2 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d + d^{3}\right)} f\right)} \sqrt{\frac{32 i \, a^{5}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left({\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} \sqrt{\frac{32 i \, a^{5}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} f e^{\left(i \, f x + i \, e\right)} + 4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right) - {\left({\left(c^{2} d - 2 i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} d + d^{3}\right)} f\right)} \sqrt{\frac{32 i \, a^{5}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left({\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} \sqrt{\frac{32 i \, a^{5}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} f e^{\left(i \, f x + i \, e\right)} + 4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right)}{{\left(2 \, c^{2} d - 4 i \, c d^{2} - 2 \, d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, {\left(c^{2} d + d^{3}\right)} f}"," ",0,"(sqrt(2)*((4*a^2*c + 4*I*a^2*d)*e^(3*I*f*x + 3*I*e) + (4*a^2*c + 4*I*a^2*d)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((c^2*d - 2*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (c^2*d + d^3)*f)*sqrt(4*I*a^5/(d^3*f^2))*log((I*d^2*f*sqrt(4*I*a^5/(d^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2) - ((c^2*d - 2*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (c^2*d + d^3)*f)*sqrt(4*I*a^5/(d^3*f^2))*log((-I*d^2*f*sqrt(4*I*a^5/(d^3*f^2))*e^(I*f*x + I*e) + sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2) + ((c^2*d - 2*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (c^2*d + d^3)*f)*sqrt(32*I*a^5/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(1/4*((I*c^2 + 2*c*d - I*d^2)*sqrt(32*I*a^5/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*f*e^(I*f*x + I*e) + 4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2) - ((c^2*d - 2*I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (c^2*d + d^3)*f)*sqrt(32*I*a^5/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(1/4*((-I*c^2 - 2*c*d + I*d^2)*sqrt(32*I*a^5/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*f*e^(I*f*x + I*e) + 4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2))/((2*c^2*d - 4*I*c*d^2 - 2*d^3)*f*e^(2*I*f*x + 2*I*e) + 2*(c^2*d + d^3)*f)","B",0
1162,1,553,0,0.450778," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(-4 i \, a e^{\left(3 i \, f x + 3 i \, e\right)} - 4 i \, a e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(c^{2} - 2 i \, c d - d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} + d^{2}\right)} f\right)} \sqrt{\frac{8 i \, a^{3}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left({\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f \sqrt{\frac{8 i \, a^{3}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + 2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right) + {\left({\left(c^{2} - 2 i \, c d - d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(c^{2} + d^{2}\right)} f\right)} \sqrt{\frac{8 i \, a^{3}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left(\frac{{\left({\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f \sqrt{\frac{8 i \, a^{3}}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + 2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right)}{{\left(2 \, c^{2} - 4 i \, c d - 2 \, d^{2}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \, {\left(c^{2} + d^{2}\right)} f}"," ",0,"-(sqrt(2)*(-4*I*a*e^(3*I*f*x + 3*I*e) - 4*I*a*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((c^2 - 2*I*c*d - d^2)*f*e^(2*I*f*x + 2*I*e) + (c^2 + d^2)*f)*sqrt(8*I*a^3/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(1/2*((I*c^2 + 2*c*d - I*d^2)*f*sqrt(8*I*a^3/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*e^(I*f*x + I*e) + 2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a) + ((c^2 - 2*I*c*d - d^2)*f*e^(2*I*f*x + 2*I*e) + (c^2 + d^2)*f)*sqrt(8*I*a^3/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(1/2*((-I*c^2 - 2*c*d + I*d^2)*f*sqrt(8*I*a^3/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*e^(I*f*x + I*e) + 2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a))/((2*c^2 - 4*I*c*d - 2*d^2)*f*e^(2*I*f*x + 2*I*e) + 2*(c^2 + d^2)*f)","B",0
1163,1,598,0,0.489264," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, d e^{\left(3 i \, f x + 3 i \, e\right)} - 4 i \, d e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(i \, c^{3} + c^{2} d + i \, c d^{2} + d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(i \, c^{3} - c^{2} d + i \, c d^{2} - d^{3}\right)} f\right)} \sqrt{\frac{2 i \, a}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left({\left({\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} f \sqrt{\frac{2 i \, a}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right) + {\left({\left(-i \, c^{3} - c^{2} d - i \, c d^{2} - d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-i \, c^{3} + c^{2} d - i \, c d^{2} + d^{3}\right)} f\right)} \sqrt{\frac{2 i \, a}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} \log\left({\left({\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} f \sqrt{\frac{2 i \, a}{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right)}{{\left(2 i \, c^{3} + 2 \, c^{2} d + 2 i \, c d^{2} + 2 \, d^{3}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 i \, c^{3} - 2 \, c^{2} d + 2 i \, c d^{2} - 2 \, d^{3}\right)} f}"," ",0,"(sqrt(2)*(-4*I*d*e^(3*I*f*x + 3*I*e) - 4*I*d*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((I*c^3 + c^2*d + I*c*d^2 + d^3)*f*e^(2*I*f*x + 2*I*e) + (I*c^3 - c^2*d + I*c*d^2 - d^3)*f)*sqrt(2*I*a/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(((I*c^2 + 2*c*d - I*d^2)*f*sqrt(2*I*a/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e)) + ((-I*c^3 - c^2*d - I*c*d^2 - d^3)*f*e^(2*I*f*x + 2*I*e) + (-I*c^3 + c^2*d - I*c*d^2 + d^3)*f)*sqrt(2*I*a/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*log(((-I*c^2 - 2*c*d + I*d^2)*f*sqrt(2*I*a/((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e)))/((2*I*c^3 + 2*c^2*d + 2*I*c*d^2 + 2*d^3)*f*e^(2*I*f*x + 2*I*e) + (2*I*c^3 - 2*c^2*d + 2*I*c*d^2 - 2*d^3)*f)","B",0
1164,1,672,0,0.566386," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(2 i \, c^{2} + 2 i \, d^{2} + {\left(2 i \, c^{2} + 4 \, c d - 10 i \, d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(4 i \, c^{2} + 4 \, c d - 8 i \, d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(a c^{4} + 2 i \, a c^{3} d + 2 i \, a c d^{3} - a d^{4}\right)} f e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{2 i}{{\left(-i \, a c^{3} - 3 \, a c^{2} d + 3 i \, a c d^{2} + a d^{3}\right)} f^{2}}} \log\left({\left(i \, a c^{2} + 2 \, a c d - i \, a d^{2}\right)} f \sqrt{\frac{2 i}{{\left(-i \, a c^{3} - 3 \, a c^{2} d + 3 i \, a c d^{2} + a d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - {\left({\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(a c^{4} + 2 i \, a c^{3} d + 2 i \, a c d^{3} - a d^{4}\right)} f e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{2 i}{{\left(-i \, a c^{3} - 3 \, a c^{2} d + 3 i \, a c d^{2} + a d^{3}\right)} f^{2}}} \log\left({\left(-i \, a c^{2} - 2 \, a c d + i \, a d^{2}\right)} f \sqrt{\frac{2 i}{{\left(-i \, a c^{3} - 3 \, a c^{2} d + 3 i \, a c d^{2} + a d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)}{4 \, {\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(4 \, a c^{4} + 8 i \, a c^{3} d + 8 i \, a c d^{3} - 4 \, a d^{4}\right)} f e^{\left(i \, f x + i \, e\right)}}"," ",0,"(sqrt(2)*(2*I*c^2 + 2*I*d^2 + (2*I*c^2 + 4*c*d - 10*I*d^2)*e^(4*I*f*x + 4*I*e) + (4*I*c^2 + 4*c*d - 8*I*d^2)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(3*I*f*x + 3*I*e) + (a*c^4 + 2*I*a*c^3*d + 2*I*a*c*d^3 - a*d^4)*f*e^(I*f*x + I*e))*sqrt(2*I/((-I*a*c^3 - 3*a*c^2*d + 3*I*a*c*d^2 + a*d^3)*f^2))*log((I*a*c^2 + 2*a*c*d - I*a*d^2)*f*sqrt(2*I/((-I*a*c^3 - 3*a*c^2*d + 3*I*a*c*d^2 + a*d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - ((a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(3*I*f*x + 3*I*e) + (a*c^4 + 2*I*a*c^3*d + 2*I*a*c*d^3 - a*d^4)*f*e^(I*f*x + I*e))*sqrt(2*I/((-I*a*c^3 - 3*a*c^2*d + 3*I*a*c*d^2 + a*d^3)*f^2))*log((-I*a*c^2 - 2*a*c*d + I*a*d^2)*f*sqrt(2*I/((-I*a*c^3 - 3*a*c^2*d + 3*I*a*c*d^2 + a*d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)))/(4*(a*c^4 + 2*a*c^2*d^2 + a*d^4)*f*e^(3*I*f*x + 3*I*e) + (4*a*c^4 + 8*I*a*c^3*d + 8*I*a*c*d^3 - 4*a*d^4)*f*e^(I*f*x + I*e))","B",0
1165,1,979,0,0.567251," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(c^{3} + i \, c^{2} d + c d^{2} + i \, d^{3} + {\left(4 \, c^{3} + 6 i \, c^{2} d + 24 \, c d^{2} - 38 i \, d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(9 \, c^{3} + 19 i \, c^{2} d + 29 \, c d^{2} - 25 i \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{3} + 14 i \, c^{2} d + 6 \, c d^{2} + 14 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(-3 i \, a^{2} c^{5} + 3 \, a^{2} c^{4} d - 6 i \, a^{2} c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3} - 3 i \, a^{2} c d^{4} + 3 \, a^{2} d^{5}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-3 i \, a^{2} c^{5} + 9 \, a^{2} c^{4} d + 6 i \, a^{2} c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3} + 9 i \, a^{2} c d^{4} - 3 \, a^{2} d^{5}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-2 i \, a^{3} c^{3} - 6 \, a^{3} c^{2} d + 6 i \, a^{3} c d^{2} + 2 \, a^{3} d^{3}\right)} f^{2}}} \log\left({\left(2 i \, a^{2} c^{2} + 4 \, a^{2} c d - 2 i \, a^{2} d^{2}\right)} f \sqrt{\frac{i}{{\left(-2 i \, a^{3} c^{3} - 6 \, a^{3} c^{2} d + 6 i \, a^{3} c d^{2} + 2 \, a^{3} d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + {\left({\left(3 i \, a^{2} c^{5} - 3 \, a^{2} c^{4} d + 6 i \, a^{2} c^{3} d^{2} - 6 \, a^{2} c^{2} d^{3} + 3 i \, a^{2} c d^{4} - 3 \, a^{2} d^{5}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(3 i \, a^{2} c^{5} - 9 \, a^{2} c^{4} d - 6 i \, a^{2} c^{3} d^{2} - 6 \, a^{2} c^{2} d^{3} - 9 i \, a^{2} c d^{4} + 3 \, a^{2} d^{5}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-2 i \, a^{3} c^{3} - 6 \, a^{3} c^{2} d + 6 i \, a^{3} c d^{2} + 2 \, a^{3} d^{3}\right)} f^{2}}} \log\left({\left(-2 i \, a^{2} c^{2} - 4 \, a^{2} c d + 2 i \, a^{2} d^{2}\right)} f \sqrt{\frac{i}{{\left(-2 i \, a^{3} c^{3} - 6 \, a^{3} c^{2} d + 6 i \, a^{3} c d^{2} + 2 \, a^{3} d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)}{{\left(-12 i \, a^{2} c^{5} + 12 \, a^{2} c^{4} d - 24 i \, a^{2} c^{3} d^{2} + 24 \, a^{2} c^{2} d^{3} - 12 i \, a^{2} c d^{4} + 12 \, a^{2} d^{5}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-12 i \, a^{2} c^{5} + 36 \, a^{2} c^{4} d + 24 i \, a^{2} c^{3} d^{2} + 24 \, a^{2} c^{2} d^{3} + 36 i \, a^{2} c d^{4} - 12 \, a^{2} d^{5}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)}}"," ",0,"(sqrt(2)*(c^3 + I*c^2*d + c*d^2 + I*d^3 + (4*c^3 + 6*I*c^2*d + 24*c*d^2 - 38*I*d^3)*e^(6*I*f*x + 6*I*e) + (9*c^3 + 19*I*c^2*d + 29*c*d^2 - 25*I*d^3)*e^(4*I*f*x + 4*I*e) + (6*c^3 + 14*I*c^2*d + 6*c*d^2 + 14*I*d^3)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((-3*I*a^2*c^5 + 3*a^2*c^4*d - 6*I*a^2*c^3*d^2 + 6*a^2*c^2*d^3 - 3*I*a^2*c*d^4 + 3*a^2*d^5)*f*e^(5*I*f*x + 5*I*e) + (-3*I*a^2*c^5 + 9*a^2*c^4*d + 6*I*a^2*c^3*d^2 + 6*a^2*c^2*d^3 + 9*I*a^2*c*d^4 - 3*a^2*d^5)*f*e^(3*I*f*x + 3*I*e))*sqrt(I/((-2*I*a^3*c^3 - 6*a^3*c^2*d + 6*I*a^3*c*d^2 + 2*a^3*d^3)*f^2))*log((2*I*a^2*c^2 + 4*a^2*c*d - 2*I*a^2*d^2)*f*sqrt(I/((-2*I*a^3*c^3 - 6*a^3*c^2*d + 6*I*a^3*c*d^2 + 2*a^3*d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + ((3*I*a^2*c^5 - 3*a^2*c^4*d + 6*I*a^2*c^3*d^2 - 6*a^2*c^2*d^3 + 3*I*a^2*c*d^4 - 3*a^2*d^5)*f*e^(5*I*f*x + 5*I*e) + (3*I*a^2*c^5 - 9*a^2*c^4*d - 6*I*a^2*c^3*d^2 - 6*a^2*c^2*d^3 - 9*I*a^2*c*d^4 + 3*a^2*d^5)*f*e^(3*I*f*x + 3*I*e))*sqrt(I/((-2*I*a^3*c^3 - 6*a^3*c^2*d + 6*I*a^3*c*d^2 + 2*a^3*d^3)*f^2))*log((-2*I*a^2*c^2 - 4*a^2*c*d + 2*I*a^2*d^2)*f*sqrt(I/((-2*I*a^3*c^3 - 6*a^3*c^2*d + 6*I*a^3*c*d^2 + 2*a^3*d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)))/((-12*I*a^2*c^5 + 12*a^2*c^4*d - 24*I*a^2*c^3*d^2 + 24*a^2*c^2*d^3 - 12*I*a^2*c*d^4 + 12*a^2*d^5)*f*e^(5*I*f*x + 5*I*e) + (-12*I*a^2*c^5 + 36*a^2*c^4*d + 24*I*a^2*c^3*d^2 + 24*a^2*c^2*d^3 + 36*I*a^2*c*d^4 - 12*a^2*d^5)*f*e^(3*I*f*x + 3*I*e))","B",0
1166,1,1082,0,0.595001," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(-3 i \, c^{4} + 6 \, c^{3} d + 6 \, c d^{3} + 3 i \, d^{4} + {\left(-23 i \, c^{4} + 68 \, c^{3} d + 18 i \, c^{2} d^{2} + 332 \, c d^{3} - 463 i \, d^{4}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(-57 i \, c^{4} + 200 \, c^{3} d + 178 i \, c^{2} d^{2} + 464 \, c d^{3} - 269 i \, d^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-48 i \, c^{4} + 172 \, c^{3} d + 172 i \, c^{2} d^{2} + 172 \, c d^{3} + 220 i \, d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-17 i \, c^{4} + 46 \, c^{3} d + 12 i \, c^{2} d^{2} + 46 \, c d^{3} + 29 i \, d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(30 \, a^{3} c^{6} + 60 i \, a^{3} c^{5} d + 30 \, a^{3} c^{4} d^{2} + 120 i \, a^{3} c^{3} d^{3} - 30 \, a^{3} c^{2} d^{4} + 60 i \, a^{3} c d^{5} - 30 \, a^{3} d^{6}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(30 \, a^{3} c^{6} + 120 i \, a^{3} c^{5} d - 150 \, a^{3} c^{4} d^{2} - 150 \, a^{3} c^{2} d^{4} - 120 i \, a^{3} c d^{5} + 30 \, a^{3} d^{6}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-8 i \, a^{5} c^{3} - 24 \, a^{5} c^{2} d + 24 i \, a^{5} c d^{2} + 8 \, a^{5} d^{3}\right)} f^{2}}} \log\left({\left(4 i \, a^{3} c^{2} + 8 \, a^{3} c d - 4 i \, a^{3} d^{2}\right)} f \sqrt{\frac{i}{{\left(-8 i \, a^{5} c^{3} - 24 \, a^{5} c^{2} d + 24 i \, a^{5} c d^{2} + 8 \, a^{5} d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + {\left({\left(30 \, a^{3} c^{6} + 60 i \, a^{3} c^{5} d + 30 \, a^{3} c^{4} d^{2} + 120 i \, a^{3} c^{3} d^{3} - 30 \, a^{3} c^{2} d^{4} + 60 i \, a^{3} c d^{5} - 30 \, a^{3} d^{6}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(30 \, a^{3} c^{6} + 120 i \, a^{3} c^{5} d - 150 \, a^{3} c^{4} d^{2} - 150 \, a^{3} c^{2} d^{4} - 120 i \, a^{3} c d^{5} + 30 \, a^{3} d^{6}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{\frac{i}{{\left(-8 i \, a^{5} c^{3} - 24 \, a^{5} c^{2} d + 24 i \, a^{5} c d^{2} + 8 \, a^{5} d^{3}\right)} f^{2}}} \log\left({\left(-4 i \, a^{3} c^{2} - 8 \, a^{3} c d + 4 i \, a^{3} d^{2}\right)} f \sqrt{\frac{i}{{\left(-8 i \, a^{5} c^{3} - 24 \, a^{5} c^{2} d + 24 i \, a^{5} c d^{2} + 8 \, a^{5} d^{3}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)}{{\left(120 \, a^{3} c^{6} + 240 i \, a^{3} c^{5} d + 120 \, a^{3} c^{4} d^{2} + 480 i \, a^{3} c^{3} d^{3} - 120 \, a^{3} c^{2} d^{4} + 240 i \, a^{3} c d^{5} - 120 \, a^{3} d^{6}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(120 \, a^{3} c^{6} + 480 i \, a^{3} c^{5} d - 600 \, a^{3} c^{4} d^{2} - 600 \, a^{3} c^{2} d^{4} - 480 i \, a^{3} c d^{5} + 120 \, a^{3} d^{6}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)}}"," ",0,"-(sqrt(2)*(-3*I*c^4 + 6*c^3*d + 6*c*d^3 + 3*I*d^4 + (-23*I*c^4 + 68*c^3*d + 18*I*c^2*d^2 + 332*c*d^3 - 463*I*d^4)*e^(8*I*f*x + 8*I*e) + (-57*I*c^4 + 200*c^3*d + 178*I*c^2*d^2 + 464*c*d^3 - 269*I*d^4)*e^(6*I*f*x + 6*I*e) + (-48*I*c^4 + 172*c^3*d + 172*I*c^2*d^2 + 172*c*d^3 + 220*I*d^4)*e^(4*I*f*x + 4*I*e) + (-17*I*c^4 + 46*c^3*d + 12*I*c^2*d^2 + 46*c*d^3 + 29*I*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((30*a^3*c^6 + 60*I*a^3*c^5*d + 30*a^3*c^4*d^2 + 120*I*a^3*c^3*d^3 - 30*a^3*c^2*d^4 + 60*I*a^3*c*d^5 - 30*a^3*d^6)*f*e^(7*I*f*x + 7*I*e) + (30*a^3*c^6 + 120*I*a^3*c^5*d - 150*a^3*c^4*d^2 - 150*a^3*c^2*d^4 - 120*I*a^3*c*d^5 + 30*a^3*d^6)*f*e^(5*I*f*x + 5*I*e))*sqrt(I/((-8*I*a^5*c^3 - 24*a^5*c^2*d + 24*I*a^5*c*d^2 + 8*a^5*d^3)*f^2))*log((4*I*a^3*c^2 + 8*a^3*c*d - 4*I*a^3*d^2)*f*sqrt(I/((-8*I*a^5*c^3 - 24*a^5*c^2*d + 24*I*a^5*c*d^2 + 8*a^5*d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + ((30*a^3*c^6 + 60*I*a^3*c^5*d + 30*a^3*c^4*d^2 + 120*I*a^3*c^3*d^3 - 30*a^3*c^2*d^4 + 60*I*a^3*c*d^5 - 30*a^3*d^6)*f*e^(7*I*f*x + 7*I*e) + (30*a^3*c^6 + 120*I*a^3*c^5*d - 150*a^3*c^4*d^2 - 150*a^3*c^2*d^4 - 120*I*a^3*c*d^5 + 30*a^3*d^6)*f*e^(5*I*f*x + 5*I*e))*sqrt(I/((-8*I*a^5*c^3 - 24*a^5*c^2*d + 24*I*a^5*c*d^2 + 8*a^5*d^3)*f^2))*log((-4*I*a^3*c^2 - 8*a^3*c*d + 4*I*a^3*d^2)*f*sqrt(I/((-8*I*a^5*c^3 - 24*a^5*c^2*d + 24*I*a^5*c*d^2 + 8*a^5*d^3)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)))/((120*a^3*c^6 + 240*I*a^3*c^5*d + 120*a^3*c^4*d^2 + 480*I*a^3*c^3*d^3 - 120*a^3*c^2*d^4 + 240*I*a^3*c*d^5 - 120*a^3*d^6)*f*e^(7*I*f*x + 7*I*e) + (120*a^3*c^6 + 480*I*a^3*c^5*d - 600*a^3*c^4*d^2 - 600*a^3*c^2*d^4 - 480*I*a^3*c*d^5 + 120*a^3*d^6)*f*e^(5*I*f*x + 5*I*e))","B",0
1167,1,866,0,0.640415," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(4 \, {\left(-i \, a^{2} c - a^{2} d\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-7 i \, a^{2} c - a^{2} d\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + 3 \, {\left(-i \, a^{2} c + a^{2} d\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(3 \, c^{4} - 12 i \, c^{3} d - 18 \, c^{2} d^{2} + 12 i \, c d^{3} + 3 \, d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} - 12 i \, c^{3} d - 12 i \, c d^{3} - 6 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f\right)} \sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left({\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} \sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} f e^{\left(i \, f x + i \, e\right)} + 4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right) + {\left({\left(3 \, c^{4} - 12 i \, c^{3} d - 18 \, c^{2} d^{2} + 12 i \, c d^{3} + 3 \, d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 \, c^{4} - 12 i \, c^{3} d - 12 i \, c d^{3} - 6 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 3 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f\right)} \sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left({\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} \sqrt{-\frac{32 i \, a^{5}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} f e^{\left(i \, f x + i \, e\right)} + 4 \, \sqrt{2} {\left(a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{4 \, a^{2}}\right)}{{\left(6 \, c^{4} - 24 i \, c^{3} d - 36 \, c^{2} d^{2} + 24 i \, c d^{3} + 6 \, d^{4}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(12 \, c^{4} - 24 i \, c^{3} d - 24 i \, c d^{3} - 12 \, d^{4}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + 6 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f}"," ",0,"-(8*sqrt(2)*(4*(-I*a^2*c - a^2*d)*e^(5*I*f*x + 5*I*e) + (-7*I*a^2*c - a^2*d)*e^(3*I*f*x + 3*I*e) + 3*(-I*a^2*c + a^2*d)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((3*c^4 - 12*I*c^3*d - 18*c^2*d^2 + 12*I*c*d^3 + 3*d^4)*f*e^(4*I*f*x + 4*I*e) + (6*c^4 - 12*I*c^3*d - 12*I*c*d^3 - 6*d^4)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4 + 2*c^2*d^2 + d^4)*f)*sqrt(-32*I*a^5/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(1/4*((I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*sqrt(-32*I*a^5/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*f*e^(I*f*x + I*e) + 4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2) + ((3*c^4 - 12*I*c^3*d - 18*c^2*d^2 + 12*I*c*d^3 + 3*d^4)*f*e^(4*I*f*x + 4*I*e) + (6*c^4 - 12*I*c^3*d - 12*I*c*d^3 - 6*d^4)*f*e^(2*I*f*x + 2*I*e) + 3*(c^4 + 2*c^2*d^2 + d^4)*f)*sqrt(-32*I*a^5/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(1/4*((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*sqrt(-32*I*a^5/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*f*e^(I*f*x + I*e) + 4*sqrt(2)*(a^2*e^(2*I*f*x + 2*I*e) + a^2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a^2))/((6*c^4 - 24*I*c^3*d - 36*c^2*d^2 + 24*I*c*d^3 + 6*d^4)*f*e^(4*I*f*x + 4*I*e) + (12*c^4 - 24*I*c^3*d - 24*I*c*d^3 - 12*d^4)*f*e^(2*I*f*x + 2*I*e) + 6*(c^4 + 2*c^2*d^2 + d^4)*f)","B",0
1168,1,1011,0,0.531839," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left({\left(3 \, a c^{2} + 2 i \, a c d + 5 \, a d^{2}\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + 2 \, {\left(3 \, a c^{2} + 4 i \, a c d + a d^{2}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + 3 \, {\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(-3 i \, c^{5} - 9 \, c^{4} d + 6 i \, c^{3} d^{2} - 6 \, c^{2} d^{3} + 9 i \, c d^{4} + 3 \, d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-6 i \, c^{5} - 6 \, c^{4} d - 12 i \, c^{3} d^{2} - 12 \, c^{2} d^{3} - 6 i \, c d^{4} - 6 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-3 i \, c^{5} + 3 \, c^{4} d - 6 i \, c^{3} d^{2} + 6 \, c^{2} d^{3} - 3 i \, c d^{4} + 3 \, d^{5}\right)} f\right)} \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left({\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + 2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right) + {\left({\left(3 i \, c^{5} + 9 \, c^{4} d - 6 i \, c^{3} d^{2} + 6 \, c^{2} d^{3} - 9 i \, c d^{4} - 3 \, d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(6 i \, c^{5} + 6 \, c^{4} d + 12 i \, c^{3} d^{2} + 12 \, c^{2} d^{3} + 6 i \, c d^{4} + 6 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(3 i \, c^{5} - 3 \, c^{4} d + 6 i \, c^{3} d^{2} - 6 \, c^{2} d^{3} + 3 i \, c d^{4} - 3 \, d^{5}\right)} f\right)} \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left(\frac{{\left({\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f \sqrt{-\frac{8 i \, a^{3}}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + 2 \, \sqrt{2} {\left(a e^{\left(2 i \, f x + 2 i \, e\right)} + a\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}\right)} e^{\left(-i \, f x - i \, e\right)}}{2 \, a}\right)}{{\left(-6 i \, c^{5} - 18 \, c^{4} d + 12 i \, c^{3} d^{2} - 12 \, c^{2} d^{3} + 18 i \, c d^{4} + 6 \, d^{5}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-12 i \, c^{5} - 12 \, c^{4} d - 24 i \, c^{3} d^{2} - 24 \, c^{2} d^{3} - 12 i \, c d^{4} - 12 \, d^{5}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(-6 i \, c^{5} + 6 \, c^{4} d - 12 i \, c^{3} d^{2} + 12 \, c^{2} d^{3} - 6 i \, c d^{4} + 6 \, d^{5}\right)} f}"," ",0,"(4*sqrt(2)*((3*a*c^2 + 2*I*a*c*d + 5*a*d^2)*e^(5*I*f*x + 5*I*e) + 2*(3*a*c^2 + 4*I*a*c*d + a*d^2)*e^(3*I*f*x + 3*I*e) + 3*(a*c^2 + 2*I*a*c*d - a*d^2)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((-3*I*c^5 - 9*c^4*d + 6*I*c^3*d^2 - 6*c^2*d^3 + 9*I*c*d^4 + 3*d^5)*f*e^(4*I*f*x + 4*I*e) + (-6*I*c^5 - 6*c^4*d - 12*I*c^3*d^2 - 12*c^2*d^3 - 6*I*c*d^4 - 6*d^5)*f*e^(2*I*f*x + 2*I*e) + (-3*I*c^5 + 3*c^4*d - 6*I*c^3*d^2 + 6*c^2*d^3 - 3*I*c*d^4 + 3*d^5)*f)*sqrt(-8*I*a^3/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(1/2*((I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f*sqrt(-8*I*a^3/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*e^(I*f*x + I*e) + 2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a) + ((3*I*c^5 + 9*c^4*d - 6*I*c^3*d^2 + 6*c^2*d^3 - 9*I*c*d^4 - 3*d^5)*f*e^(4*I*f*x + 4*I*e) + (6*I*c^5 + 6*c^4*d + 12*I*c^3*d^2 + 12*c^2*d^3 + 6*I*c*d^4 + 6*d^5)*f*e^(2*I*f*x + 2*I*e) + (3*I*c^5 - 3*c^4*d + 6*I*c^3*d^2 - 6*c^2*d^3 + 3*I*c*d^4 - 3*d^5)*f)*sqrt(-8*I*a^3/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(1/2*((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*sqrt(-8*I*a^3/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*e^(I*f*x + I*e) + 2*sqrt(2)*(a*e^(2*I*f*x + 2*I*e) + a)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)))*e^(-I*f*x - I*e)/a))/((-6*I*c^5 - 18*c^4*d + 12*I*c^3*d^2 - 12*c^2*d^3 + 18*I*c*d^4 + 6*d^5)*f*e^(4*I*f*x + 4*I*e) + (-12*I*c^5 - 12*c^4*d - 24*I*c^3*d^2 - 24*c^2*d^3 - 12*I*c*d^4 - 12*d^5)*f*e^(2*I*f*x + 2*I*e) + (-6*I*c^5 + 6*c^4*d - 12*I*c^3*d^2 + 12*c^2*d^3 - 6*I*c*d^4 + 6*d^5)*f)","B",0
1169,1,988,0,0.555595," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(24 \, c^{2} d - 16 i \, c d^{2} + 8 \, d^{3}\right)} e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(48 \, c^{2} d + 8 i \, c d^{2} + 8 \, d^{3}\right)} e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(24 \, c^{2} d + 24 i \, c d^{2}\right)} e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(3 \, c^{6} - 6 i \, c^{5} d + 3 \, c^{4} d^{2} - 12 i \, c^{3} d^{3} - 3 \, c^{2} d^{4} - 6 i \, c d^{5} - 3 \, d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + 6 \, {\left(c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(3 \, c^{6} + 6 i \, c^{5} d + 3 \, c^{4} d^{2} + 12 i \, c^{3} d^{3} - 3 \, c^{2} d^{4} + 6 i \, c d^{5} - 3 \, d^{6}\right)} f\right)} \sqrt{-\frac{2 i \, a}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left({\left({\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} f \sqrt{-\frac{2 i \, a}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right) + {\left({\left(3 \, c^{6} - 6 i \, c^{5} d + 3 \, c^{4} d^{2} - 12 i \, c^{3} d^{3} - 3 \, c^{2} d^{4} - 6 i \, c d^{5} - 3 \, d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + 6 \, {\left(c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(3 \, c^{6} + 6 i \, c^{5} d + 3 \, c^{4} d^{2} + 12 i \, c^{3} d^{3} - 3 \, c^{2} d^{4} + 6 i \, c d^{5} - 3 \, d^{6}\right)} f\right)} \sqrt{-\frac{2 i \, a}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} \log\left({\left({\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} f \sqrt{-\frac{2 i \, a}{{\left(i \, c^{5} + 5 \, c^{4} d - 10 i \, c^{3} d^{2} - 10 \, c^{2} d^{3} + 5 i \, c d^{4} + d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)} e^{\left(-i \, f x - i \, e\right)}\right)}{{\left(6 \, c^{6} - 12 i \, c^{5} d + 6 \, c^{4} d^{2} - 24 i \, c^{3} d^{3} - 6 \, c^{2} d^{4} - 12 i \, c d^{5} - 6 \, d^{6}\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + 12 \, {\left(c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 \, c^{6} + 12 i \, c^{5} d + 6 \, c^{4} d^{2} + 24 i \, c^{3} d^{3} - 6 \, c^{2} d^{4} + 12 i \, c d^{5} - 6 \, d^{6}\right)} f}"," ",0,"-(sqrt(2)*((24*c^2*d - 16*I*c*d^2 + 8*d^3)*e^(5*I*f*x + 5*I*e) + (48*c^2*d + 8*I*c*d^2 + 8*d^3)*e^(3*I*f*x + 3*I*e) + (24*c^2*d + 24*I*c*d^2)*e^(I*f*x + I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((3*c^6 - 6*I*c^5*d + 3*c^4*d^2 - 12*I*c^3*d^3 - 3*c^2*d^4 - 6*I*c*d^5 - 3*d^6)*f*e^(4*I*f*x + 4*I*e) + 6*(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6)*f*e^(2*I*f*x + 2*I*e) + (3*c^6 + 6*I*c^5*d + 3*c^4*d^2 + 12*I*c^3*d^3 - 3*c^2*d^4 + 6*I*c*d^5 - 3*d^6)*f)*sqrt(-2*I*a/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(((I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*f*sqrt(-2*I*a/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e)) + ((3*c^6 - 6*I*c^5*d + 3*c^4*d^2 - 12*I*c^3*d^3 - 3*c^2*d^4 - 6*I*c*d^5 - 3*d^6)*f*e^(4*I*f*x + 4*I*e) + 6*(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6)*f*e^(2*I*f*x + 2*I*e) + (3*c^6 + 6*I*c^5*d + 3*c^4*d^2 + 12*I*c^3*d^3 - 3*c^2*d^4 + 6*I*c*d^5 - 3*d^6)*f)*sqrt(-2*I*a/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*log(((-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*f*sqrt(-2*I*a/((I*c^5 + 5*c^4*d - 10*I*c^3*d^2 - 10*c^2*d^3 + 5*I*c*d^4 + d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1))*e^(-I*f*x - I*e)))/((6*c^6 - 12*I*c^5*d + 6*c^4*d^2 - 24*I*c^3*d^3 - 6*c^2*d^4 - 12*I*c*d^5 - 6*d^6)*f*e^(4*I*f*x + 4*I*e) + 12*(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6)*f*e^(2*I*f*x + 2*I*e) + (6*c^6 + 12*I*c^5*d + 6*c^4*d^2 + 24*I*c^3*d^3 - 6*c^2*d^4 + 12*I*c*d^5 - 6*d^6)*f)","B",0
1170,1,1304,0,0.641364," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(6 \, c^{4} + 12 \, c^{2} d^{2} + 6 \, d^{4} + {\left(6 \, c^{4} - 24 i \, c^{3} d - 108 \, c^{2} d^{2} + 104 i \, c d^{3} + 14 \, d^{4}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(18 \, c^{4} - 48 i \, c^{3} d - 180 \, c^{2} d^{2} + 32 i \, c d^{3} - 22 \, d^{4}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(18 \, c^{4} - 24 i \, c^{3} d - 60 \, c^{2} d^{2} - 72 i \, c d^{3} - 30 \, d^{4}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} - {\left({\left(3 i \, a c^{7} + 3 \, a c^{6} d + 9 i \, a c^{5} d^{2} + 9 \, a c^{4} d^{3} + 9 i \, a c^{3} d^{4} + 9 \, a c^{2} d^{5} + 3 i \, a c d^{6} + 3 \, a d^{7}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(6 i \, a c^{7} - 6 \, a c^{6} d + 18 i \, a c^{5} d^{2} - 18 \, a c^{4} d^{3} + 18 i \, a c^{3} d^{4} - 18 \, a c^{2} d^{5} + 6 i \, a c d^{6} - 6 \, a d^{7}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(3 i \, a c^{7} - 9 \, a c^{6} d - 3 i \, a c^{5} d^{2} - 15 \, a c^{4} d^{3} - 15 i \, a c^{3} d^{4} - 3 \, a c^{2} d^{5} - 9 i \, a c d^{6} + 3 \, a d^{7}\right)} f e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{-\frac{2 i}{{\left(i \, a c^{5} + 5 \, a c^{4} d - 10 i \, a c^{3} d^{2} - 10 \, a c^{2} d^{3} + 5 i \, a c d^{4} + a d^{5}\right)} f^{2}}} \log\left({\left(i \, a c^{3} + 3 \, a c^{2} d - 3 i \, a c d^{2} - a d^{3}\right)} f \sqrt{-\frac{2 i}{{\left(i \, a c^{5} + 5 \, a c^{4} d - 10 i \, a c^{3} d^{2} - 10 \, a c^{2} d^{3} + 5 i \, a c d^{4} + a d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - {\left({\left(-3 i \, a c^{7} - 3 \, a c^{6} d - 9 i \, a c^{5} d^{2} - 9 \, a c^{4} d^{3} - 9 i \, a c^{3} d^{4} - 9 \, a c^{2} d^{5} - 3 i \, a c d^{6} - 3 \, a d^{7}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(-6 i \, a c^{7} + 6 \, a c^{6} d - 18 i \, a c^{5} d^{2} + 18 \, a c^{4} d^{3} - 18 i \, a c^{3} d^{4} + 18 \, a c^{2} d^{5} - 6 i \, a c d^{6} + 6 \, a d^{7}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(-3 i \, a c^{7} + 9 \, a c^{6} d + 3 i \, a c^{5} d^{2} + 15 \, a c^{4} d^{3} + 15 i \, a c^{3} d^{4} + 3 \, a c^{2} d^{5} + 9 i \, a c d^{6} - 3 \, a d^{7}\right)} f e^{\left(i \, f x + i \, e\right)}\right)} \sqrt{-\frac{2 i}{{\left(i \, a c^{5} + 5 \, a c^{4} d - 10 i \, a c^{3} d^{2} - 10 \, a c^{2} d^{3} + 5 i \, a c d^{4} + a d^{5}\right)} f^{2}}} \log\left({\left(-i \, a c^{3} - 3 \, a c^{2} d + 3 i \, a c d^{2} + a d^{3}\right)} f \sqrt{-\frac{2 i}{{\left(i \, a c^{5} + 5 \, a c^{4} d - 10 i \, a c^{3} d^{2} - 10 \, a c^{2} d^{3} + 5 i \, a c d^{4} + a d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)}{{\left(12 i \, a c^{7} + 12 \, a c^{6} d + 36 i \, a c^{5} d^{2} + 36 \, a c^{4} d^{3} + 36 i \, a c^{3} d^{4} + 36 \, a c^{2} d^{5} + 12 i \, a c d^{6} + 12 \, a d^{7}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(24 i \, a c^{7} - 24 \, a c^{6} d + 72 i \, a c^{5} d^{2} - 72 \, a c^{4} d^{3} + 72 i \, a c^{3} d^{4} - 72 \, a c^{2} d^{5} + 24 i \, a c d^{6} - 24 \, a d^{7}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)} + {\left(12 i \, a c^{7} - 36 \, a c^{6} d - 12 i \, a c^{5} d^{2} - 60 \, a c^{4} d^{3} - 60 i \, a c^{3} d^{4} - 12 \, a c^{2} d^{5} - 36 i \, a c d^{6} + 12 \, a d^{7}\right)} f e^{\left(i \, f x + i \, e\right)}}"," ",0,"-(sqrt(2)*(6*c^4 + 12*c^2*d^2 + 6*d^4 + (6*c^4 - 24*I*c^3*d - 108*c^2*d^2 + 104*I*c*d^3 + 14*d^4)*e^(6*I*f*x + 6*I*e) + (18*c^4 - 48*I*c^3*d - 180*c^2*d^2 + 32*I*c*d^3 - 22*d^4)*e^(4*I*f*x + 4*I*e) + (18*c^4 - 24*I*c^3*d - 60*c^2*d^2 - 72*I*c*d^3 - 30*d^4)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) - ((3*I*a*c^7 + 3*a*c^6*d + 9*I*a*c^5*d^2 + 9*a*c^4*d^3 + 9*I*a*c^3*d^4 + 9*a*c^2*d^5 + 3*I*a*c*d^6 + 3*a*d^7)*f*e^(5*I*f*x + 5*I*e) + (6*I*a*c^7 - 6*a*c^6*d + 18*I*a*c^5*d^2 - 18*a*c^4*d^3 + 18*I*a*c^3*d^4 - 18*a*c^2*d^5 + 6*I*a*c*d^6 - 6*a*d^7)*f*e^(3*I*f*x + 3*I*e) + (3*I*a*c^7 - 9*a*c^6*d - 3*I*a*c^5*d^2 - 15*a*c^4*d^3 - 15*I*a*c^3*d^4 - 3*a*c^2*d^5 - 9*I*a*c*d^6 + 3*a*d^7)*f*e^(I*f*x + I*e))*sqrt(-2*I/((I*a*c^5 + 5*a*c^4*d - 10*I*a*c^3*d^2 - 10*a*c^2*d^3 + 5*I*a*c*d^4 + a*d^5)*f^2))*log((I*a*c^3 + 3*a*c^2*d - 3*I*a*c*d^2 - a*d^3)*f*sqrt(-2*I/((I*a*c^5 + 5*a*c^4*d - 10*I*a*c^3*d^2 - 10*a*c^2*d^3 + 5*I*a*c*d^4 + a*d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - ((-3*I*a*c^7 - 3*a*c^6*d - 9*I*a*c^5*d^2 - 9*a*c^4*d^3 - 9*I*a*c^3*d^4 - 9*a*c^2*d^5 - 3*I*a*c*d^6 - 3*a*d^7)*f*e^(5*I*f*x + 5*I*e) + (-6*I*a*c^7 + 6*a*c^6*d - 18*I*a*c^5*d^2 + 18*a*c^4*d^3 - 18*I*a*c^3*d^4 + 18*a*c^2*d^5 - 6*I*a*c*d^6 + 6*a*d^7)*f*e^(3*I*f*x + 3*I*e) + (-3*I*a*c^7 + 9*a*c^6*d + 3*I*a*c^5*d^2 + 15*a*c^4*d^3 + 15*I*a*c^3*d^4 + 3*a*c^2*d^5 + 9*I*a*c*d^6 - 3*a*d^7)*f*e^(I*f*x + I*e))*sqrt(-2*I/((I*a*c^5 + 5*a*c^4*d - 10*I*a*c^3*d^2 - 10*a*c^2*d^3 + 5*I*a*c*d^4 + a*d^5)*f^2))*log((-I*a*c^3 - 3*a*c^2*d + 3*I*a*c*d^2 + a*d^3)*f*sqrt(-2*I/((I*a*c^5 + 5*a*c^4*d - 10*I*a*c^3*d^2 - 10*a*c^2*d^3 + 5*I*a*c*d^4 + a*d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)))/((12*I*a*c^7 + 12*a*c^6*d + 36*I*a*c^5*d^2 + 36*a*c^4*d^3 + 36*I*a*c^3*d^4 + 36*a*c^2*d^5 + 12*I*a*c*d^6 + 12*a*d^7)*f*e^(5*I*f*x + 5*I*e) + (24*I*a*c^7 - 24*a*c^6*d + 72*I*a*c^5*d^2 - 72*a*c^4*d^3 + 72*I*a*c^3*d^4 - 72*a*c^2*d^5 + 24*I*a*c*d^6 - 24*a*d^7)*f*e^(3*I*f*x + 3*I*e) + (12*I*a*c^7 - 36*a*c^6*d - 12*I*a*c^5*d^2 - 60*a*c^4*d^3 - 60*I*a*c^3*d^4 - 12*a*c^2*d^5 - 36*I*a*c*d^6 + 12*a*d^7)*f*e^(I*f*x + I*e))","B",0
1171,1,1551,0,0.658923," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(i \, c^{5} - c^{4} d + 2 i \, c^{3} d^{2} - 2 \, c^{2} d^{3} + i \, c d^{4} - d^{5} + {\left(4 i \, c^{5} - 4 \, c^{4} d + 56 i \, c^{3} d^{2} + 200 \, c^{2} d^{3} - 204 i \, c d^{4} - 52 \, d^{5}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(13 i \, c^{5} - 25 \, c^{4} d + 134 i \, c^{3} d^{2} + 314 \, c^{2} d^{3} - 87 i \, c d^{4} + 35 \, d^{5}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(15 i \, c^{5} - 39 \, c^{4} d + 90 i \, c^{3} d^{2} + 78 \, c^{2} d^{3} + 123 i \, c d^{4} + 69 \, d^{5}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(7 i \, c^{5} - 19 \, c^{4} d + 14 i \, c^{3} d^{2} - 38 \, c^{2} d^{3} + 7 i \, c d^{4} - 19 \, d^{5}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left(3 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(6 \, a^{2} c^{8} + 12 i \, a^{2} c^{7} d + 12 \, a^{2} c^{6} d^{2} + 36 i \, a^{2} c^{5} d^{3} + 36 i \, a^{2} c^{3} d^{5} - 12 \, a^{2} c^{2} d^{6} + 12 i \, a^{2} c d^{7} - 6 \, a^{2} d^{8}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(3 \, a^{2} c^{8} + 12 i \, a^{2} c^{7} d - 12 \, a^{2} c^{6} d^{2} + 12 i \, a^{2} c^{5} d^{3} - 30 \, a^{2} c^{4} d^{4} - 12 i \, a^{2} c^{3} d^{5} - 12 \, a^{2} c^{2} d^{6} - 12 i \, a^{2} c d^{7} + 3 \, a^{2} d^{8}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(2 i \, a^{3} c^{5} + 10 \, a^{3} c^{4} d - 20 i \, a^{3} c^{3} d^{2} - 20 \, a^{3} c^{2} d^{3} + 10 i \, a^{3} c d^{4} + 2 \, a^{3} d^{5}\right)} f^{2}}} \log\left({\left(2 i \, a^{2} c^{3} + 6 \, a^{2} c^{2} d - 6 i \, a^{2} c d^{2} - 2 \, a^{2} d^{3}\right)} f \sqrt{-\frac{i}{{\left(2 i \, a^{3} c^{5} + 10 \, a^{3} c^{4} d - 20 i \, a^{3} c^{3} d^{2} - 20 \, a^{3} c^{2} d^{3} + 10 i \, a^{3} c d^{4} + 2 \, a^{3} d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) - {\left(3 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(6 \, a^{2} c^{8} + 12 i \, a^{2} c^{7} d + 12 \, a^{2} c^{6} d^{2} + 36 i \, a^{2} c^{5} d^{3} + 36 i \, a^{2} c^{3} d^{5} - 12 \, a^{2} c^{2} d^{6} + 12 i \, a^{2} c d^{7} - 6 \, a^{2} d^{8}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(3 \, a^{2} c^{8} + 12 i \, a^{2} c^{7} d - 12 \, a^{2} c^{6} d^{2} + 12 i \, a^{2} c^{5} d^{3} - 30 \, a^{2} c^{4} d^{4} - 12 i \, a^{2} c^{3} d^{5} - 12 \, a^{2} c^{2} d^{6} - 12 i \, a^{2} c d^{7} + 3 \, a^{2} d^{8}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(2 i \, a^{3} c^{5} + 10 \, a^{3} c^{4} d - 20 i \, a^{3} c^{3} d^{2} - 20 \, a^{3} c^{2} d^{3} + 10 i \, a^{3} c d^{4} + 2 \, a^{3} d^{5}\right)} f^{2}}} \log\left({\left(-2 i \, a^{2} c^{3} - 6 \, a^{2} c^{2} d + 6 i \, a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} f \sqrt{-\frac{i}{{\left(2 i \, a^{3} c^{5} + 10 \, a^{3} c^{4} d - 20 i \, a^{3} c^{3} d^{2} - 20 \, a^{3} c^{2} d^{3} + 10 i \, a^{3} c d^{4} + 2 \, a^{3} d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)}{12 \, {\left(a^{2} c^{8} + 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} + 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(24 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d + 48 \, a^{2} c^{6} d^{2} + 144 i \, a^{2} c^{5} d^{3} + 144 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} + 48 i \, a^{2} c d^{7} - 24 \, a^{2} d^{8}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)} + {\left(12 \, a^{2} c^{8} + 48 i \, a^{2} c^{7} d - 48 \, a^{2} c^{6} d^{2} + 48 i \, a^{2} c^{5} d^{3} - 120 \, a^{2} c^{4} d^{4} - 48 i \, a^{2} c^{3} d^{5} - 48 \, a^{2} c^{2} d^{6} - 48 i \, a^{2} c d^{7} + 12 \, a^{2} d^{8}\right)} f e^{\left(3 i \, f x + 3 i \, e\right)}}"," ",0,"(sqrt(2)*(I*c^5 - c^4*d + 2*I*c^3*d^2 - 2*c^2*d^3 + I*c*d^4 - d^5 + (4*I*c^5 - 4*c^4*d + 56*I*c^3*d^2 + 200*c^2*d^3 - 204*I*c*d^4 - 52*d^5)*e^(8*I*f*x + 8*I*e) + (13*I*c^5 - 25*c^4*d + 134*I*c^3*d^2 + 314*c^2*d^3 - 87*I*c*d^4 + 35*d^5)*e^(6*I*f*x + 6*I*e) + (15*I*c^5 - 39*c^4*d + 90*I*c^3*d^2 + 78*c^2*d^3 + 123*I*c*d^4 + 69*d^5)*e^(4*I*f*x + 4*I*e) + (7*I*c^5 - 19*c^4*d + 14*I*c^3*d^2 - 38*c^2*d^3 + 7*I*c*d^4 - 19*d^5)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + (3*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(7*I*f*x + 7*I*e) + (6*a^2*c^8 + 12*I*a^2*c^7*d + 12*a^2*c^6*d^2 + 36*I*a^2*c^5*d^3 + 36*I*a^2*c^3*d^5 - 12*a^2*c^2*d^6 + 12*I*a^2*c*d^7 - 6*a^2*d^8)*f*e^(5*I*f*x + 5*I*e) + (3*a^2*c^8 + 12*I*a^2*c^7*d - 12*a^2*c^6*d^2 + 12*I*a^2*c^5*d^3 - 30*a^2*c^4*d^4 - 12*I*a^2*c^3*d^5 - 12*a^2*c^2*d^6 - 12*I*a^2*c*d^7 + 3*a^2*d^8)*f*e^(3*I*f*x + 3*I*e))*sqrt(-I/((2*I*a^3*c^5 + 10*a^3*c^4*d - 20*I*a^3*c^3*d^2 - 20*a^3*c^2*d^3 + 10*I*a^3*c*d^4 + 2*a^3*d^5)*f^2))*log((2*I*a^2*c^3 + 6*a^2*c^2*d - 6*I*a^2*c*d^2 - 2*a^2*d^3)*f*sqrt(-I/((2*I*a^3*c^5 + 10*a^3*c^4*d - 20*I*a^3*c^3*d^2 - 20*a^3*c^2*d^3 + 10*I*a^3*c*d^4 + 2*a^3*d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) - (3*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(7*I*f*x + 7*I*e) + (6*a^2*c^8 + 12*I*a^2*c^7*d + 12*a^2*c^6*d^2 + 36*I*a^2*c^5*d^3 + 36*I*a^2*c^3*d^5 - 12*a^2*c^2*d^6 + 12*I*a^2*c*d^7 - 6*a^2*d^8)*f*e^(5*I*f*x + 5*I*e) + (3*a^2*c^8 + 12*I*a^2*c^7*d - 12*a^2*c^6*d^2 + 12*I*a^2*c^5*d^3 - 30*a^2*c^4*d^4 - 12*I*a^2*c^3*d^5 - 12*a^2*c^2*d^6 - 12*I*a^2*c*d^7 + 3*a^2*d^8)*f*e^(3*I*f*x + 3*I*e))*sqrt(-I/((2*I*a^3*c^5 + 10*a^3*c^4*d - 20*I*a^3*c^3*d^2 - 20*a^3*c^2*d^3 + 10*I*a^3*c*d^4 + 2*a^3*d^5)*f^2))*log((-2*I*a^2*c^3 - 6*a^2*c^2*d + 6*I*a^2*c*d^2 + 2*a^2*d^3)*f*sqrt(-I/((2*I*a^3*c^5 + 10*a^3*c^4*d - 20*I*a^3*c^3*d^2 - 20*a^3*c^2*d^3 + 10*I*a^3*c*d^4 + 2*a^3*d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)))/(12*(a^2*c^8 + 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 + 4*a^2*c^2*d^6 + a^2*d^8)*f*e^(7*I*f*x + 7*I*e) + (24*a^2*c^8 + 48*I*a^2*c^7*d + 48*a^2*c^6*d^2 + 144*I*a^2*c^5*d^3 + 144*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 + 48*I*a^2*c*d^7 - 24*a^2*d^8)*f*e^(5*I*f*x + 5*I*e) + (12*a^2*c^8 + 48*I*a^2*c^7*d - 48*a^2*c^6*d^2 + 48*I*a^2*c^5*d^3 - 120*a^2*c^4*d^4 - 48*I*a^2*c^3*d^5 - 48*a^2*c^2*d^6 - 48*I*a^2*c*d^7 + 12*a^2*d^8)*f*e^(3*I*f*x + 3*I*e))","B",0
1172,1,1770,0,0.714192," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(3 \, c^{6} + 6 i \, c^{5} d + 3 \, c^{4} d^{2} + 12 i \, c^{3} d^{3} - 3 \, c^{2} d^{4} + 6 i \, c d^{5} - 3 \, d^{6} + {\left(23 \, c^{6} + 62 i \, c^{5} d + 55 \, c^{4} d^{2} + 860 i \, c^{3} d^{3} + 3145 \, c^{2} d^{4} - 3298 i \, c d^{5} - 983 \, d^{6}\right)} e^{\left(10 i \, f x + 10 i \, e\right)} + {\left(80 \, c^{6} + 284 i \, c^{5} d - 80 \, c^{4} d^{2} + 2360 i \, c^{3} d^{3} + 4960 \, c^{2} d^{4} - 1540 i \, c d^{5} + 544 \, d^{6}\right)} e^{\left(8 i \, f x + 8 i \, e\right)} + {\left(105 \, c^{6} + 426 i \, c^{5} d - 387 \, c^{4} d^{2} + 1908 i \, c^{3} d^{3} + 1167 \, c^{2} d^{4} + 1962 i \, c d^{5} + 1179 \, d^{6}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(65 \, c^{6} + 254 i \, c^{5} d - 251 \, c^{4} d^{2} + 508 i \, c^{3} d^{3} - 697 \, c^{2} d^{4} + 254 i \, c d^{5} - 381 \, d^{6}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(20 \, c^{6} + 56 i \, c^{5} d + 4 \, c^{4} d^{2} + 112 i \, c^{3} d^{3} - 52 \, c^{2} d^{4} + 56 i \, c d^{5} - 36 \, d^{6}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} + {\left({\left(-30 i \, a^{3} c^{9} + 30 \, a^{3} c^{8} d - 120 i \, a^{3} c^{7} d^{2} + 120 \, a^{3} c^{6} d^{3} - 180 i \, a^{3} c^{5} d^{4} + 180 \, a^{3} c^{4} d^{5} - 120 i \, a^{3} c^{3} d^{6} + 120 \, a^{3} c^{2} d^{7} - 30 i \, a^{3} c d^{8} + 30 \, a^{3} d^{9}\right)} f e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-60 i \, a^{3} c^{9} + 180 \, a^{3} c^{8} d + 480 \, a^{3} c^{6} d^{3} + 360 i \, a^{3} c^{5} d^{4} + 360 \, a^{3} c^{4} d^{5} + 480 i \, a^{3} c^{3} d^{6} + 180 i \, a^{3} c d^{8} - 60 \, a^{3} d^{9}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-30 i \, a^{3} c^{9} + 150 \, a^{3} c^{8} d + 240 i \, a^{3} c^{7} d^{2} + 420 i \, a^{3} c^{5} d^{4} - 420 \, a^{3} c^{4} d^{5} - 240 \, a^{3} c^{2} d^{7} - 150 i \, a^{3} c d^{8} + 30 \, a^{3} d^{9}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(8 i \, a^{5} c^{5} + 40 \, a^{5} c^{4} d - 80 i \, a^{5} c^{3} d^{2} - 80 \, a^{5} c^{2} d^{3} + 40 i \, a^{5} c d^{4} + 8 \, a^{5} d^{5}\right)} f^{2}}} \log\left({\left(4 i \, a^{3} c^{3} + 12 \, a^{3} c^{2} d - 12 i \, a^{3} c d^{2} - 4 \, a^{3} d^{3}\right)} f \sqrt{-\frac{i}{{\left(8 i \, a^{5} c^{5} + 40 \, a^{5} c^{4} d - 80 i \, a^{5} c^{3} d^{2} - 80 \, a^{5} c^{2} d^{3} + 40 i \, a^{5} c d^{4} + 8 \, a^{5} d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right) + {\left({\left(30 i \, a^{3} c^{9} - 30 \, a^{3} c^{8} d + 120 i \, a^{3} c^{7} d^{2} - 120 \, a^{3} c^{6} d^{3} + 180 i \, a^{3} c^{5} d^{4} - 180 \, a^{3} c^{4} d^{5} + 120 i \, a^{3} c^{3} d^{6} - 120 \, a^{3} c^{2} d^{7} + 30 i \, a^{3} c d^{8} - 30 \, a^{3} d^{9}\right)} f e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(60 i \, a^{3} c^{9} - 180 \, a^{3} c^{8} d - 480 \, a^{3} c^{6} d^{3} - 360 i \, a^{3} c^{5} d^{4} - 360 \, a^{3} c^{4} d^{5} - 480 i \, a^{3} c^{3} d^{6} - 180 i \, a^{3} c d^{8} + 60 \, a^{3} d^{9}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(30 i \, a^{3} c^{9} - 150 \, a^{3} c^{8} d - 240 i \, a^{3} c^{7} d^{2} - 420 i \, a^{3} c^{5} d^{4} + 420 \, a^{3} c^{4} d^{5} + 240 \, a^{3} c^{2} d^{7} + 150 i \, a^{3} c d^{8} - 30 \, a^{3} d^{9}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} \sqrt{-\frac{i}{{\left(8 i \, a^{5} c^{5} + 40 \, a^{5} c^{4} d - 80 i \, a^{5} c^{3} d^{2} - 80 \, a^{5} c^{2} d^{3} + 40 i \, a^{5} c d^{4} + 8 \, a^{5} d^{5}\right)} f^{2}}} \log\left({\left(-4 i \, a^{3} c^{3} - 12 \, a^{3} c^{2} d + 12 i \, a^{3} c d^{2} + 4 \, a^{3} d^{3}\right)} f \sqrt{-\frac{i}{{\left(8 i \, a^{5} c^{5} + 40 \, a^{5} c^{4} d - 80 i \, a^{5} c^{3} d^{2} - 80 \, a^{5} c^{2} d^{3} + 40 i \, a^{5} c d^{4} + 8 \, a^{5} d^{5}\right)} f^{2}}} e^{\left(i \, f x + i \, e\right)} + \sqrt{2} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} \sqrt{\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}\right)}{{\left(-120 i \, a^{3} c^{9} + 120 \, a^{3} c^{8} d - 480 i \, a^{3} c^{7} d^{2} + 480 \, a^{3} c^{6} d^{3} - 720 i \, a^{3} c^{5} d^{4} + 720 \, a^{3} c^{4} d^{5} - 480 i \, a^{3} c^{3} d^{6} + 480 \, a^{3} c^{2} d^{7} - 120 i \, a^{3} c d^{8} + 120 \, a^{3} d^{9}\right)} f e^{\left(9 i \, f x + 9 i \, e\right)} + {\left(-240 i \, a^{3} c^{9} + 720 \, a^{3} c^{8} d + 1920 \, a^{3} c^{6} d^{3} + 1440 i \, a^{3} c^{5} d^{4} + 1440 \, a^{3} c^{4} d^{5} + 1920 i \, a^{3} c^{3} d^{6} + 720 i \, a^{3} c d^{8} - 240 \, a^{3} d^{9}\right)} f e^{\left(7 i \, f x + 7 i \, e\right)} + {\left(-120 i \, a^{3} c^{9} + 600 \, a^{3} c^{8} d + 960 i \, a^{3} c^{7} d^{2} + 1680 i \, a^{3} c^{5} d^{4} - 1680 \, a^{3} c^{4} d^{5} - 960 \, a^{3} c^{2} d^{7} - 600 i \, a^{3} c d^{8} + 120 \, a^{3} d^{9}\right)} f e^{\left(5 i \, f x + 5 i \, e\right)}}"," ",0,"(sqrt(2)*(3*c^6 + 6*I*c^5*d + 3*c^4*d^2 + 12*I*c^3*d^3 - 3*c^2*d^4 + 6*I*c*d^5 - 3*d^6 + (23*c^6 + 62*I*c^5*d + 55*c^4*d^2 + 860*I*c^3*d^3 + 3145*c^2*d^4 - 3298*I*c*d^5 - 983*d^6)*e^(10*I*f*x + 10*I*e) + (80*c^6 + 284*I*c^5*d - 80*c^4*d^2 + 2360*I*c^3*d^3 + 4960*c^2*d^4 - 1540*I*c*d^5 + 544*d^6)*e^(8*I*f*x + 8*I*e) + (105*c^6 + 426*I*c^5*d - 387*c^4*d^2 + 1908*I*c^3*d^3 + 1167*c^2*d^4 + 1962*I*c*d^5 + 1179*d^6)*e^(6*I*f*x + 6*I*e) + (65*c^6 + 254*I*c^5*d - 251*c^4*d^2 + 508*I*c^3*d^3 - 697*c^2*d^4 + 254*I*c*d^5 - 381*d^6)*e^(4*I*f*x + 4*I*e) + (20*c^6 + 56*I*c^5*d + 4*c^4*d^2 + 112*I*c^3*d^3 - 52*c^2*d^4 + 56*I*c*d^5 - 36*d^6)*e^(2*I*f*x + 2*I*e))*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1)) + ((-30*I*a^3*c^9 + 30*a^3*c^8*d - 120*I*a^3*c^7*d^2 + 120*a^3*c^6*d^3 - 180*I*a^3*c^5*d^4 + 180*a^3*c^4*d^5 - 120*I*a^3*c^3*d^6 + 120*a^3*c^2*d^7 - 30*I*a^3*c*d^8 + 30*a^3*d^9)*f*e^(9*I*f*x + 9*I*e) + (-60*I*a^3*c^9 + 180*a^3*c^8*d + 480*a^3*c^6*d^3 + 360*I*a^3*c^5*d^4 + 360*a^3*c^4*d^5 + 480*I*a^3*c^3*d^6 + 180*I*a^3*c*d^8 - 60*a^3*d^9)*f*e^(7*I*f*x + 7*I*e) + (-30*I*a^3*c^9 + 150*a^3*c^8*d + 240*I*a^3*c^7*d^2 + 420*I*a^3*c^5*d^4 - 420*a^3*c^4*d^5 - 240*a^3*c^2*d^7 - 150*I*a^3*c*d^8 + 30*a^3*d^9)*f*e^(5*I*f*x + 5*I*e))*sqrt(-I/((8*I*a^5*c^5 + 40*a^5*c^4*d - 80*I*a^5*c^3*d^2 - 80*a^5*c^2*d^3 + 40*I*a^5*c*d^4 + 8*a^5*d^5)*f^2))*log((4*I*a^3*c^3 + 12*a^3*c^2*d - 12*I*a^3*c*d^2 - 4*a^3*d^3)*f*sqrt(-I/((8*I*a^5*c^5 + 40*a^5*c^4*d - 80*I*a^5*c^3*d^2 - 80*a^5*c^2*d^3 + 40*I*a^5*c*d^4 + 8*a^5*d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)) + ((30*I*a^3*c^9 - 30*a^3*c^8*d + 120*I*a^3*c^7*d^2 - 120*a^3*c^6*d^3 + 180*I*a^3*c^5*d^4 - 180*a^3*c^4*d^5 + 120*I*a^3*c^3*d^6 - 120*a^3*c^2*d^7 + 30*I*a^3*c*d^8 - 30*a^3*d^9)*f*e^(9*I*f*x + 9*I*e) + (60*I*a^3*c^9 - 180*a^3*c^8*d - 480*a^3*c^6*d^3 - 360*I*a^3*c^5*d^4 - 360*a^3*c^4*d^5 - 480*I*a^3*c^3*d^6 - 180*I*a^3*c*d^8 + 60*a^3*d^9)*f*e^(7*I*f*x + 7*I*e) + (30*I*a^3*c^9 - 150*a^3*c^8*d - 240*I*a^3*c^7*d^2 - 420*I*a^3*c^5*d^4 + 420*a^3*c^4*d^5 + 240*a^3*c^2*d^7 + 150*I*a^3*c*d^8 - 30*a^3*d^9)*f*e^(5*I*f*x + 5*I*e))*sqrt(-I/((8*I*a^5*c^5 + 40*a^5*c^4*d - 80*I*a^5*c^3*d^2 - 80*a^5*c^2*d^3 + 40*I*a^5*c*d^4 + 8*a^5*d^5)*f^2))*log((-4*I*a^3*c^3 - 12*a^3*c^2*d + 12*I*a^3*c*d^2 + 4*a^3*d^3)*f*sqrt(-I/((8*I*a^5*c^5 + 40*a^5*c^4*d - 80*I*a^5*c^3*d^2 - 80*a^5*c^2*d^3 + 40*I*a^5*c*d^4 + 8*a^5*d^5)*f^2))*e^(I*f*x + I*e) + sqrt(2)*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*sqrt(a/(e^(2*I*f*x + 2*I*e) + 1))*(e^(2*I*f*x + 2*I*e) + 1)))/((-120*I*a^3*c^9 + 120*a^3*c^8*d - 480*I*a^3*c^7*d^2 + 480*a^3*c^6*d^3 - 720*I*a^3*c^5*d^4 + 720*a^3*c^4*d^5 - 480*I*a^3*c^3*d^6 + 480*a^3*c^2*d^7 - 120*I*a^3*c*d^8 + 120*a^3*d^9)*f*e^(9*I*f*x + 9*I*e) + (-240*I*a^3*c^9 + 720*a^3*c^8*d + 1920*a^3*c^6*d^3 + 1440*I*a^3*c^5*d^4 + 1440*a^3*c^4*d^5 + 1920*I*a^3*c^3*d^6 + 720*I*a^3*c*d^8 - 240*a^3*d^9)*f*e^(7*I*f*x + 7*I*e) + (-120*I*a^3*c^9 + 600*a^3*c^8*d + 960*I*a^3*c^7*d^2 + 1680*I*a^3*c^5*d^4 - 1680*a^3*c^4*d^5 - 960*a^3*c^2*d^7 - 600*I*a^3*c*d^8 + 120*a^3*d^9)*f*e^(5*I*f*x + 5*I*e))","B",0
1173,0,0,0,1.136392," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n, x)","F",0
1174,0,0,0,0.474682," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, a^{3} \left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(6 i \, f x + 6 i \, e\right)}}{e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(8*a^3*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(6*I*f*x + 6*I*e)/(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1175,0,0,0,0.442954," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, a^{2} \left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(4 i \, f x + 4 i \, e\right)}}{e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(4*a^2*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(4*I*f*x + 4*I*e)/(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1176,0,0,0,0.599956," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*a*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1177,0,0,0,0.548166," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(2*I*f*x + 2*I*e) + 1)*e^(-2*I*f*x - 2*I*e)/a, x)","F",0
1178,0,0,0,0.502588," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)*e^(-4*I*f*x - 4*I*e)/a^2, x)","F",0
1179,0,0,0,0.484419," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{n} {\left(e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))^n*(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1)*e^(-6*I*f*x - 6*I*e)/a^3, x)","F",0
1180,0,0,0,0.501998," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{3} + 3 i \, c^{2} d - 3 \, c d^{2} - i \, d^{3} + {\left(c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(3 \, c^{3} - 3 i \, c^{2} d + 3 \, c d^{2} - 3 i \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(3 \, c^{3} + 3 i \, c^{2} d + 3 \, c d^{2} + 3 i \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral((c^3 + 3*I*c^2*d - 3*c*d^2 - I*d^3 + (c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)*e^(6*I*f*x + 6*I*e) + (3*c^3 - 3*I*c^2*d + 3*c*d^2 - 3*I*d^3)*e^(4*I*f*x + 4*I*e) + (3*c^3 + 3*I*c^2*d + 3*c*d^2 + 3*I*d^3)*e^(2*I*f*x + 2*I*e))*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1181,0,0,0,0.779513," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} + 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(c^{2} + d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral((c^2 + 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(4*I*f*x + 4*I*e) + 2*(c^2 + d^2)*e^(2*I*f*x + 2*I*e))*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1182,0,0,0,0.649393," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1183,0,0,0,0.726556," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}}{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(I*e^(2*I*f*x + 2*I*e) + I)/((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d), x)","F",0
1184,0,0,0,0.592127," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{c^{2} + 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(c^{2} + d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)/(c^2 + 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(4*I*f*x + 4*I*e) + 2*(c^2 + d^2)*e^(2*I*f*x + 2*I*e)), x)","F",0
1185,0,0,0,0.547475," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} {\left(-i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 3 i \, e^{\left(2 i \, f x + 2 i \, e\right)} - i\right)}}{-i \, c^{3} + 3 \, c^{2} d + 3 i \, c d^{2} - d^{3} + {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-3 i \, c^{3} - 3 \, c^{2} d - 3 i \, c d^{2} - 3 \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-3 i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} + 3 \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*(-I*e^(6*I*f*x + 6*I*e) - 3*I*e^(4*I*f*x + 4*I*e) - 3*I*e^(2*I*f*x + 2*I*e) - I)/(-I*c^3 + 3*c^2*d + 3*I*c*d^2 - d^3 + (-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*e^(6*I*f*x + 6*I*e) + (-3*I*c^3 - 3*c^2*d - 3*I*c*d^2 - 3*d^3)*e^(4*I*f*x + 4*I*e) + (-3*I*c^3 + 3*c^2*d - 3*I*c*d^2 + 3*d^3)*e^(2*I*f*x + 2*I*e)), x)","F",0
1186,0,0,0,0.545147," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d\right)} \left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)*(2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1187,0,0,0,0.507139," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1)), x)","F",0
1188,0,0,0,0.563539," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)}}{{\left(i \, c + d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i \, c - d}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(I*e^(2*I*f*x + 2*I*e) + I)/((I*c + d)*e^(2*I*f*x + 2*I*e) + I*c - d), x)","F",0
1189,0,0,0,0.498799," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}}{c^{2} + 2 i \, c d - d^{2} + {\left(c^{2} - 2 i \, c d - d^{2}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, {\left(c^{2} + d^{2}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)/(c^2 + 2*I*c*d - d^2 + (c^2 - 2*I*c*d - d^2)*e^(4*I*f*x + 4*I*e) + 2*(c^2 + d^2)*e^(2*I*f*x + 2*I*e)), x)","F",0
1190,0,0,0,0.487816," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} \sqrt{\frac{{\left(c - i \, d\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + c + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}} {\left(-i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 3 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 3 i \, e^{\left(2 i \, f x + 2 i \, e\right)} - i\right)}}{-i \, c^{3} + 3 \, c^{2} d + 3 i \, c d^{2} - d^{3} + {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(-3 i \, c^{3} - 3 \, c^{2} d - 3 i \, c d^{2} - 3 \, d^{3}\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(-3 i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} + 3 \, d^{3}\right)} e^{\left(2 i \, f x + 2 i \, e\right)}}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*sqrt(((c - I*d)*e^(2*I*f*x + 2*I*e) + c + I*d)/(e^(2*I*f*x + 2*I*e) + 1))*(-I*e^(6*I*f*x + 6*I*e) - 3*I*e^(4*I*f*x + 4*I*e) - 3*I*e^(2*I*f*x + 2*I*e) - I)/(-I*c^3 + 3*c^2*d + 3*I*c*d^2 - d^3 + (-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*e^(6*I*f*x + 6*I*e) + (-3*I*c^3 - 3*c^2*d - 3*I*c*d^2 - 3*d^3)*e^(4*I*f*x + 4*I*e) + (-3*I*c^3 + 3*c^2*d - 3*I*c*d^2 + 3*d^3)*e^(2*I*f*x + 2*I*e)), x)","F",0
1191,1,147,0,0.426751," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, b^{3} d \tan\left(f x + e\right)^{3} + 6 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c - {\left(3 \, a^{2} b - b^{3}\right)} d\right)} f x + 3 \, {\left(b^{3} c + 3 \, a b^{2} d\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c + {\left(a^{3} - 3 \, a b^{2}\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(3 \, a b^{2} c + {\left(3 \, a^{2} b - b^{3}\right)} d\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*b^3*d*tan(f*x + e)^3 + 6*((a^3 - 3*a*b^2)*c - (3*a^2*b - b^3)*d)*f*x + 3*(b^3*c + 3*a*b^2*d)*tan(f*x + e)^2 - 3*((3*a^2*b - b^3)*c + (a^3 - 3*a*b^2)*d)*log(1/(tan(f*x + e)^2 + 1)) + 6*(3*a*b^2*c + (3*a^2*b - b^3)*d)*tan(f*x + e))/f","A",0
1192,1,92,0,0.498404," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{b^{2} d \tan\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f x - {\left(2 \, a b c + {\left(a^{2} - b^{2}\right)} d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(b^{2} c + 2 \, a b d\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(b^2*d*tan(f*x + e)^2 - 2*(2*a*b*d - (a^2 - b^2)*c)*f*x - (2*a*b*c + (a^2 - b^2)*d)*log(1/(tan(f*x + e)^2 + 1)) + 2*(b^2*c + 2*a*b*d)*tan(f*x + e))/f","A",0
1193,1,50,0,0.467942," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(a c - b d\right)} f x + 2 \, b d \tan\left(f x + e\right) - {\left(b c + a d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, f}"," ",0,"1/2*(2*(a*c - b*d)*f*x + 2*b*d*tan(f*x + e) - (b*c + a*d)*log(1/(tan(f*x + e)^2 + 1)))/f","A",0
1194,1,75,0,0.721442," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(a c + b d\right)} f x + {\left(b c - a d\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(a^{2} + b^{2}\right)} f}"," ",0,"1/2*(2*(a*c + b*d)*f*x + (b*c - a*d)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)))/((a^2 + b^2)*f)","A",0
1195,1,225,0,0.483784," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} c - 2 \, a b^{2} d - 2 \, {\left(2 \, a^{2} b d + {\left(a^{3} - a b^{2}\right)} c\right)} f x - {\left(2 \, a^{2} b c - {\left(a^{3} - a b^{2}\right)} d + {\left(2 \, a b^{2} c - {\left(a^{2} b - b^{3}\right)} d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(a b^{2} c - a^{2} b d + {\left(2 \, a b^{2} d + {\left(a^{2} b - b^{3}\right)} c\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)}}"," ",0,"-1/2*(2*b^3*c - 2*a*b^2*d - 2*(2*a^2*b*d + (a^3 - a*b^2)*c)*f*x - (2*a^2*b*c - (a^3 - a*b^2)*d + (2*a*b^2*c - (a^2*b - b^3)*d)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - 2*(a*b^2*c - a^2*b*d + (2*a*b^2*d + (a^2*b - b^3)*c)*f*x)*tan(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f)","B",0
1196,1,501,0,1.506113," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{5} - 3 \, a^{3} b^{2}\right)} c + {\left(3 \, a^{4} b - a^{2} b^{3}\right)} d\right)} f x + {\left(2 \, {\left({\left(a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(3 \, a^{2} b^{3} - b^{5}\right)} d\right)} f x + {\left(5 \, a^{2} b^{3} - b^{5}\right)} c - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} d\right)} \tan\left(f x + e\right)^{2} - {\left(7 \, a^{2} b^{3} + b^{5}\right)} c + {\left(5 \, a^{3} b^{2} - a b^{4}\right)} d + {\left({\left({\left(3 \, a^{2} b^{3} - b^{5}\right)} c - {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d\right)} \tan\left(f x + e\right)^{2} + {\left(3 \, a^{4} b - a^{2} b^{3}\right)} c - {\left(a^{5} - 3 \, a^{3} b^{2}\right)} d + 2 \, {\left({\left(3 \, a^{3} b^{2} - a b^{4}\right)} c - {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(2 \, {\left({\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c + {\left(3 \, a^{3} b^{2} - a b^{4}\right)} d\right)} f x + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c - {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} d\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} f \tan\left(f x + e\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} f\right)}}"," ",0,"1/2*(2*((a^5 - 3*a^3*b^2)*c + (3*a^4*b - a^2*b^3)*d)*f*x + (2*((a^3*b^2 - 3*a*b^4)*c + (3*a^2*b^3 - b^5)*d)*f*x + (5*a^2*b^3 - b^5)*c - 3*(a^3*b^2 - a*b^4)*d)*tan(f*x + e)^2 - (7*a^2*b^3 + b^5)*c + (5*a^3*b^2 - a*b^4)*d + (((3*a^2*b^3 - b^5)*c - (a^3*b^2 - 3*a*b^4)*d)*tan(f*x + e)^2 + (3*a^4*b - a^2*b^3)*c - (a^5 - 3*a^3*b^2)*d + 2*((3*a^3*b^2 - a*b^4)*c - (a^4*b - 3*a^2*b^3)*d)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + 2*(2*((a^4*b - 3*a^2*b^3)*c + (3*a^3*b^2 - a*b^4)*d)*f*x + 3*(a^3*b^2 - a*b^4)*c - (2*a^4*b - 3*a^2*b^3 + b^5)*d)*tan(f*x + e))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*f*tan(f*x + e)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*f*tan(f*x + e) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*f)","B",0
1197,1,252,0,0.507262," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, b^{3} d^{2} \tan\left(f x + e\right)^{4} + 4 \, {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} \tan\left(f x + e\right)^{3} + 12 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{2} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} f x + 6 \, {\left(b^{3} c^{2} + 6 \, a b^{2} c d + {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d - {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left(3 \, a b^{2} c^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*b^3*d^2*tan(f*x + e)^4 + 4*(2*b^3*c*d + 3*a*b^2*d^2)*tan(f*x + e)^3 + 12*((a^3 - 3*a*b^2)*c^2 - 2*(3*a^2*b - b^3)*c*d - (a^3 - 3*a*b^2)*d^2)*f*x + 6*(b^3*c^2 + 6*a*b^2*c*d + (3*a^2*b - b^3)*d^2)*tan(f*x + e)^2 - 6*((3*a^2*b - b^3)*c^2 + 2*(a^3 - 3*a*b^2)*c*d - (3*a^2*b - b^3)*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 12*(3*a*b^2*c^2 + 2*(3*a^2*b - b^3)*c*d + (a^3 - 3*a*b^2)*d^2)*tan(f*x + e))/f","A",0
1198,1,158,0,0.490935," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} \tan\left(f x + e\right)^{3} - 3 \, {\left(4 \, a b c d - {\left(a^{2} - b^{2}\right)} c^{2} + {\left(a^{2} - b^{2}\right)} d^{2}\right)} f x + 3 \, {\left(b^{2} c d + a b d^{2}\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left(a b c^{2} - a b d^{2} + {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 3 \, {\left(b^{2} c^{2} + 4 \, a b c d + {\left(a^{2} - b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*(b^2*d^2*tan(f*x + e)^3 - 3*(4*a*b*c*d - (a^2 - b^2)*c^2 + (a^2 - b^2)*d^2)*f*x + 3*(b^2*c*d + a*b*d^2)*tan(f*x + e)^2 - 3*(a*b*c^2 - a*b*d^2 + (a^2 - b^2)*c*d)*log(1/(tan(f*x + e)^2 + 1)) + 3*(b^2*c^2 + 4*a*b*c*d + (a^2 - b^2)*d^2)*tan(f*x + e))/f","A",0
1199,1,91,0,0.468252," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{b d^{2} \tan\left(f x + e\right)^{2} + 2 \, {\left(a c^{2} - 2 \, b c d - a d^{2}\right)} f x - {\left(b c^{2} + 2 \, a c d - b d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(2 \, b c d + a d^{2}\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(b*d^2*tan(f*x + e)^2 + 2*(a*c^2 - 2*b*c*d - a*d^2)*f*x - (b*c^2 + 2*a*c*d - b*d^2)*log(1/(tan(f*x + e)^2 + 1)) + 2*(2*b*c*d + a*d^2)*tan(f*x + e))/f","A",0
1200,1,129,0,0.510411," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} d^{2} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(a b c^{2} + 2 \, b^{2} c d - a b d^{2}\right)} f x - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(a^{2} b + b^{3}\right)} f}"," ",0,"-1/2*((a^2 + b^2)*d^2*log(1/(tan(f*x + e)^2 + 1)) - 2*(a*b*c^2 + 2*b^2*c*d - a*b*d^2)*f*x - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)))/((a^2*b + b^3)*f)","A",0
1201,1,304,0,0.494592," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2} - {\left(4 \, a^{2} b c d + {\left(a^{3} - a b^{2}\right)} c^{2} - {\left(a^{3} - a b^{2}\right)} d^{2}\right)} f x - {\left(a^{2} b c^{2} - a^{2} b d^{2} - {\left(a^{3} - a b^{2}\right)} c d + {\left(a b^{2} c^{2} - a b^{2} d^{2} - {\left(a^{2} b - b^{3}\right)} c d\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(4 \, a b^{2} c d + {\left(a^{2} b - b^{3}\right)} c^{2} - {\left(a^{2} b - b^{3}\right)} d^{2}\right)} f x\right)} \tan\left(f x + e\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f}"," ",0,"-(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2 - (4*a^2*b*c*d + (a^3 - a*b^2)*c^2 - (a^3 - a*b^2)*d^2)*f*x - (a^2*b*c^2 - a^2*b*d^2 - (a^3 - a*b^2)*c*d + (a*b^2*c^2 - a*b^2*d^2 - (a^2*b - b^3)*c*d)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (4*a*b^2*c*d + (a^2*b - b^3)*c^2 - (a^2*b - b^3)*d^2)*f*x)*tan(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f)","B",0
1202,1,706,0,0.452665," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(7 \, a^{2} b^{3} + b^{5}\right)} c^{2} - 2 \, {\left(5 \, a^{3} b^{2} - a b^{4}\right)} c d + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} d^{2} - 2 \, {\left({\left(a^{5} - 3 \, a^{3} b^{2}\right)} c^{2} + 2 \, {\left(3 \, a^{4} b - a^{2} b^{3}\right)} c d - {\left(a^{5} - 3 \, a^{3} b^{2}\right)} d^{2}\right)} f x - {\left({\left(5 \, a^{2} b^{3} - b^{5}\right)} c^{2} - 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d + {\left(a^{4} b - 5 \, a^{2} b^{3}\right)} d^{2} + 2 \, {\left({\left(a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} + 2 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} c d - {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d^{2}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left({\left(3 \, a^{4} b - a^{2} b^{3}\right)} c^{2} - 2 \, {\left(a^{5} - 3 \, a^{3} b^{2}\right)} c d - {\left(3 \, a^{4} b - a^{2} b^{3}\right)} d^{2} + {\left({\left(3 \, a^{2} b^{3} - b^{5}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} c d - {\left(3 \, a^{2} b^{3} - b^{5}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, a^{3} b^{2} - a b^{4}\right)} c^{2} - 2 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c d - {\left(3 \, a^{3} b^{2} - a b^{4}\right)} d^{2}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} c d + {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} d^{2} + 2 \, {\left({\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c^{2} + 2 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} c d - {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} d^{2}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} f \tan\left(f x + e\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} f\right)}}"," ",0,"-1/2*((7*a^2*b^3 + b^5)*c^2 - 2*(5*a^3*b^2 - a*b^4)*c*d + 3*(a^4*b - a^2*b^3)*d^2 - 2*((a^5 - 3*a^3*b^2)*c^2 + 2*(3*a^4*b - a^2*b^3)*c*d - (a^5 - 3*a^3*b^2)*d^2)*f*x - ((5*a^2*b^3 - b^5)*c^2 - 6*(a^3*b^2 - a*b^4)*c*d + (a^4*b - 5*a^2*b^3)*d^2 + 2*((a^3*b^2 - 3*a*b^4)*c^2 + 2*(3*a^2*b^3 - b^5)*c*d - (a^3*b^2 - 3*a*b^4)*d^2)*f*x)*tan(f*x + e)^2 - ((3*a^4*b - a^2*b^3)*c^2 - 2*(a^5 - 3*a^3*b^2)*c*d - (3*a^4*b - a^2*b^3)*d^2 + ((3*a^2*b^3 - b^5)*c^2 - 2*(a^3*b^2 - 3*a*b^4)*c*d - (3*a^2*b^3 - b^5)*d^2)*tan(f*x + e)^2 + 2*((3*a^3*b^2 - a*b^4)*c^2 - 2*(a^4*b - 3*a^2*b^3)*c*d - (3*a^3*b^2 - a*b^4)*d^2)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - 2*(3*(a^3*b^2 - a*b^4)*c^2 - 2*(2*a^4*b - 3*a^2*b^3 + b^5)*c*d + (a^5 - 3*a^3*b^2 + 2*a*b^4)*d^2 + 2*((a^4*b - 3*a^2*b^3)*c^2 + 2*(3*a^3*b^2 - a*b^4)*c*d - (a^4*b - 3*a^2*b^3)*d^2)*f*x)*tan(f*x + e))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*f*tan(f*x + e)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*f*tan(f*x + e) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*f)","B",0
1203,1,374,0,0.534073," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{12 \, b^{3} d^{3} \tan\left(f x + e\right)^{5} + 45 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left(3 \, b^{3} c^{2} d + 9 \, a b^{2} c d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)^{3} + 60 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{3} - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} f x + 30 \, {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - 30 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 60 \, {\left(3 \, a b^{2} c^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*b^3*d^3*tan(f*x + e)^5 + 45*(b^3*c*d^2 + a*b^2*d^3)*tan(f*x + e)^4 + 20*(3*b^3*c^2*d + 9*a*b^2*c*d^2 + (3*a^2*b - b^3)*d^3)*tan(f*x + e)^3 + 60*((a^3 - 3*a*b^2)*c^3 - 3*(3*a^2*b - b^3)*c^2*d - 3*(a^3 - 3*a*b^2)*c*d^2 + (3*a^2*b - b^3)*d^3)*f*x + 30*(b^3*c^3 + 9*a*b^2*c^2*d + 3*(3*a^2*b - b^3)*c*d^2 + (a^3 - 3*a*b^2)*d^3)*tan(f*x + e)^2 - 30*((3*a^2*b - b^3)*c^3 + 3*(a^3 - 3*a*b^2)*c^2*d - 3*(3*a^2*b - b^3)*c*d^2 - (a^3 - 3*a*b^2)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 60*(3*a*b^2*c^3 + 3*(3*a^2*b - b^3)*c^2*d + 3*(a^3 - 3*a*b^2)*c*d^2 - (3*a^2*b - b^3)*d^3)*tan(f*x + e))/f","A",0
1204,1,245,0,1.539810," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{3} \tan\left(f x + e\right)^{4} + 4 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} \tan\left(f x + e\right)^{3} - 12 \, {\left(6 \, a b c^{2} d - 2 \, a b d^{3} - {\left(a^{2} - b^{2}\right)} c^{3} + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f x + 6 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + {\left(a^{2} - b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left(2 \, a b c^{3} - 6 \, a b c d^{2} + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d - {\left(a^{2} - b^{2}\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 12 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d - 2 \, a b d^{3} + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*b^2*d^3*tan(f*x + e)^4 + 4*(3*b^2*c*d^2 + 2*a*b*d^3)*tan(f*x + e)^3 - 12*(6*a*b*c^2*d - 2*a*b*d^3 - (a^2 - b^2)*c^3 + 3*(a^2 - b^2)*c*d^2)*f*x + 6*(3*b^2*c^2*d + 6*a*b*c*d^2 + (a^2 - b^2)*d^3)*tan(f*x + e)^2 - 6*(2*a*b*c^3 - 6*a*b*c*d^2 + 3*(a^2 - b^2)*c^2*d - (a^2 - b^2)*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 12*(b^2*c^3 + 6*a*b*c^2*d - 2*a*b*d^3 + 3*(a^2 - b^2)*c*d^2)*tan(f*x + e))/f","A",0
1205,1,142,0,0.551917," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, b d^{3} \tan\left(f x + e\right)^{3} + 6 \, {\left(a c^{3} - 3 \, b c^{2} d - 3 \, a c d^{2} + b d^{3}\right)} f x + 3 \, {\left(3 \, b c d^{2} + a d^{3}\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left(b c^{3} + 3 \, a c^{2} d - 3 \, b c d^{2} - a d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 6 \, {\left(3 \, b c^{2} d + 3 \, a c d^{2} - b d^{3}\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*b*d^3*tan(f*x + e)^3 + 6*(a*c^3 - 3*b*c^2*d - 3*a*c*d^2 + b*d^3)*f*x + 3*(3*b*c*d^2 + a*d^3)*tan(f*x + e)^2 - 3*(b*c^3 + 3*a*c^2*d - 3*b*c*d^2 - a*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 6*(3*b*c^2*d + 3*a*c*d^2 - b*d^3)*tan(f*x + e))/f","A",0
1206,1,201,0,0.564072," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b + b^{3}\right)} d^{3} \tan\left(f x + e\right) + 2 \, {\left(a b^{2} c^{3} + 3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} - b^{3} d^{3}\right)} f x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} - {\left(a^{3} + a b^{2}\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(a^{2} b^{2} + b^{4}\right)} f}"," ",0,"1/2*(2*(a^2*b + b^3)*d^3*tan(f*x + e) + 2*(a*b^2*c^3 + 3*b^3*c^2*d - 3*a*b^2*c*d^2 - b^3*d^3)*f*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (3*(a^2*b + b^3)*c*d^2 - (a^3 + a*b^2)*d^3)*log(1/(tan(f*x + e)^2 + 1)))/((a^2*b^2 + b^4)*f)","A",0
1207,1,501,0,0.595206," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{5} c^{3} - 6 \, a b^{4} c^{2} d + 6 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b^{2} d^{3} - 2 \, {\left(6 \, a^{2} b^{3} c^{2} d - 2 \, a^{2} b^{3} d^{3} + {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{2}\right)} f x - {\left(2 \, a^{2} b^{3} c^{3} - 6 \, a^{2} b^{3} c d^{2} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d + {\left(a^{5} + 3 \, a^{3} b^{2}\right)} d^{3} + {\left(2 \, a b^{4} c^{3} - 6 \, a b^{4} c d^{2} - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d + {\left(a^{4} b + 3 \, a^{2} b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3} + {\left(6 \, a b^{4} c^{2} d - 2 \, a b^{4} d^{3} + {\left(a^{2} b^{3} - b^{5}\right)} c^{3} - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c d^{2}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} f \tan\left(f x + e\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} f\right)}}"," ",0,"-1/2*(2*b^5*c^3 - 6*a*b^4*c^2*d + 6*a^2*b^3*c*d^2 - 2*a^3*b^2*d^3 - 2*(6*a^2*b^3*c^2*d - 2*a^2*b^3*d^3 + (a^3*b^2 - a*b^4)*c^3 - 3*(a^3*b^2 - a*b^4)*c*d^2)*f*x - (2*a^2*b^3*c^3 - 6*a^2*b^3*c*d^2 - 3*(a^3*b^2 - a*b^4)*c^2*d + (a^5 + 3*a^3*b^2)*d^3 + (2*a*b^4*c^3 - 6*a*b^4*c*d^2 - 3*(a^2*b^3 - b^5)*c^2*d + (a^4*b + 3*a^2*b^3)*d^3)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + ((a^4*b + 2*a^2*b^3 + b^5)*d^3*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*d^3)*log(1/(tan(f*x + e)^2 + 1)) - 2*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3 + (6*a*b^4*c^2*d - 2*a*b^4*d^3 + (a^2*b^3 - b^5)*c^3 - 3*(a^2*b^3 - b^5)*c*d^2)*f*x)*tan(f*x + e))/((a^4*b^3 + 2*a^2*b^5 + b^7)*f*tan(f*x + e) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*f)","B",0
1208,1,898,0,1.051536," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(7 \, a^{2} b^{3} + b^{5}\right)} c^{3} - 3 \, {\left(5 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d + 9 \, {\left(a^{4} b - a^{2} b^{3}\right)} c d^{2} - {\left(a^{5} - 5 \, a^{3} b^{2}\right)} d^{3} - 2 \, {\left({\left(a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{4} b - a^{2} b^{3}\right)} c^{2} d - 3 \, {\left(a^{5} - 3 \, a^{3} b^{2}\right)} c d^{2} - {\left(3 \, a^{4} b - a^{2} b^{3}\right)} d^{3}\right)} f x - {\left({\left(5 \, a^{2} b^{3} - b^{5}\right)} c^{3} - 9 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{2} d + 3 \, {\left(a^{4} b - 5 \, a^{2} b^{3}\right)} c d^{2} + {\left(a^{5} + 7 \, a^{3} b^{2}\right)} d^{3} + 2 \, {\left({\left(a^{3} b^{2} - 3 \, a b^{4}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} c^{2} d - 3 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} c d^{2} - {\left(3 \, a^{2} b^{3} - b^{5}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left({\left(3 \, a^{4} b - a^{2} b^{3}\right)} c^{3} - 3 \, {\left(a^{5} - 3 \, a^{3} b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{4} b - a^{2} b^{3}\right)} c d^{2} + {\left(a^{5} - 3 \, a^{3} b^{2}\right)} d^{3} + {\left({\left(3 \, a^{2} b^{3} - b^{5}\right)} c^{3} - 3 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} c d^{2} + {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, a^{3} b^{2} - a b^{4}\right)} c^{3} - 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c^{2} d - 3 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} c d^{2} + {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(3 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} - 3 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} c^{2} d + 3 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c d^{2} + 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} d^{3} + 2 \, {\left({\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c^{3} + 3 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d - 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c d^{2} - {\left(3 \, a^{3} b^{2} - a b^{4}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} f \tan\left(f x + e\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} f\right)}}"," ",0,"-1/2*((7*a^2*b^3 + b^5)*c^3 - 3*(5*a^3*b^2 - a*b^4)*c^2*d + 9*(a^4*b - a^2*b^3)*c*d^2 - (a^5 - 5*a^3*b^2)*d^3 - 2*((a^5 - 3*a^3*b^2)*c^3 + 3*(3*a^4*b - a^2*b^3)*c^2*d - 3*(a^5 - 3*a^3*b^2)*c*d^2 - (3*a^4*b - a^2*b^3)*d^3)*f*x - ((5*a^2*b^3 - b^5)*c^3 - 9*(a^3*b^2 - a*b^4)*c^2*d + 3*(a^4*b - 5*a^2*b^3)*c*d^2 + (a^5 + 7*a^3*b^2)*d^3 + 2*((a^3*b^2 - 3*a*b^4)*c^3 + 3*(3*a^2*b^3 - b^5)*c^2*d - 3*(a^3*b^2 - 3*a*b^4)*c*d^2 - (3*a^2*b^3 - b^5)*d^3)*f*x)*tan(f*x + e)^2 - ((3*a^4*b - a^2*b^3)*c^3 - 3*(a^5 - 3*a^3*b^2)*c^2*d - 3*(3*a^4*b - a^2*b^3)*c*d^2 + (a^5 - 3*a^3*b^2)*d^3 + ((3*a^2*b^3 - b^5)*c^3 - 3*(a^3*b^2 - 3*a*b^4)*c^2*d - 3*(3*a^2*b^3 - b^5)*c*d^2 + (a^3*b^2 - 3*a*b^4)*d^3)*tan(f*x + e)^2 + 2*((3*a^3*b^2 - a*b^4)*c^3 - 3*(a^4*b - 3*a^2*b^3)*c^2*d - 3*(3*a^3*b^2 - a*b^4)*c*d^2 + (a^4*b - 3*a^2*b^3)*d^3)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - 2*(3*(a^3*b^2 - a*b^4)*c^3 - 3*(2*a^4*b - 3*a^2*b^3 + b^5)*c^2*d + 3*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c*d^2 + 3*(a^4*b - a^2*b^3)*d^3 + 2*((a^4*b - 3*a^2*b^3)*c^3 + 3*(3*a^3*b^2 - a*b^4)*c^2*d - 3*(a^4*b - 3*a^2*b^3)*c*d^2 - (3*a^3*b^2 - a*b^4)*d^3)*f*x)*tan(f*x + e))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*f*tan(f*x + e)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*f*tan(f*x + e) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*f)","B",0
1209,1,299,0,0.722337," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{4}\right)} f x + {\left(b^{4} c^{2} d^{2} + b^{4} d^{4}\right)} \tan\left(f x + e\right)^{2} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a b^{3} c d^{3} + {\left(6 \, a^{2} b^{2} - b^{4}\right)} d^{4}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} + b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} \tan\left(f x + e\right)}{2 \, {\left(c^{2} d^{3} + d^{5}\right)} f}"," ",0,"1/2*(2*((a^4 - 6*a^2*b^2 + b^4)*c*d^3 + 4*(a^3*b - a*b^3)*d^4)*f*x + (b^4*c^2*d^2 + b^4*d^4)*tan(f*x + e)^2 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c*d^3 + (6*a^2*b^2 - b^4)*d^4)*log(1/(tan(f*x + e)^2 + 1)) - 2*(b^4*c^3*d - 4*a*b^3*c^2*d^2 + b^4*c*d^3 - 4*a*b^3*d^4)*tan(f*x + e))/((c^2*d^3 + d^5)*f)","A",0
1210,1,206,0,0.622701," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} f x - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(b^{3} c^{2} d + b^{3} d^{3}\right)} \tan\left(f x + e\right)}{2 \, {\left(c^{2} d^{2} + d^{4}\right)} f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c*d^2 + (3*a^2*b - b^3)*d^3)*f*x - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) + (b^3*c^3 - 3*a*b^2*c^2*d + b^3*c*d^2 - 3*a*b^2*d^3)*log(1/(tan(f*x + e)^2 + 1)) + 2*(b^3*c^2*d + b^3*d^3)*tan(f*x + e))/((c^2*d^2 + d^4)*f)","A",0
1211,1,133,0,0.511606," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a b d^{2} + {\left(a^{2} - b^{2}\right)} c d\right)} f x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(b^{2} c^{2} + b^{2} d^{2}\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(c^{2} d + d^{3}\right)} f}"," ",0,"1/2*(2*(2*a*b*d^2 + (a^2 - b^2)*c*d)*f*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (b^2*c^2 + b^2*d^2)*log(1/(tan(f*x + e)^2 + 1)))/((c^2*d + d^3)*f)","A",0
1212,1,76,0,0.503545," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(a c + b d\right)} f x - {\left(b c - a d\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left(c^{2} + d^{2}\right)} f}"," ",0,"1/2*(2*(a*c + b*d)*f*x - (b*c - a*d)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)))/((c^2 + d^2)*f)","A",0
1213,1,201,0,1.094239," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} d^{2} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(a b c^{2} + a b d^{2} - {\left(a^{2} + b^{2}\right)} c d\right)} f x - {\left(b^{2} c^{2} + b^{2} d^{2}\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right)}{2 \, {\left({\left(a^{2} b + b^{3}\right)} c^{3} - {\left(a^{3} + a b^{2}\right)} c^{2} d + {\left(a^{2} b + b^{3}\right)} c d^{2} - {\left(a^{3} + a b^{2}\right)} d^{3}\right)} f}"," ",0,"-1/2*((a^2 + b^2)*d^2*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(a*b*c^2 + a*b*d^2 - (a^2 + b^2)*c*d)*f*x - (b^2*c^2 + b^2*d^2)*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)))/(((a^2*b + b^3)*c^3 - (a^3 + a*b^2)*c^2*d + (a^2*b + b^3)*c*d^2 - (a^3 + a*b^2)*d^3)*f)","A",0
1214,1,756,0,0.936087," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, b^{5} c^{3} - 2 \, a b^{4} c^{2} d + 2 \, b^{5} c d^{2} - 2 \, a b^{4} d^{3} + 2 \, {\left(2 \, a^{4} b c^{2} d + 2 \, a^{4} b d^{3} - {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} - {\left(a^{5} + 3 \, a^{3} b^{2}\right)} c d^{2}\right)} f x - {\left(2 \, a^{2} b^{3} c^{3} + 2 \, a^{2} b^{3} c d^{2} - {\left(3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} d - {\left(3 \, a^{3} b^{2} + a b^{4}\right)} d^{3} + {\left(2 \, a b^{4} c^{3} + 2 \, a b^{4} c d^{2} - {\left(3 \, a^{2} b^{3} + b^{5}\right)} c^{2} d - {\left(3 \, a^{2} b^{3} + b^{5}\right)} d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \tan\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(a b^{4} c^{3} - a^{2} b^{3} c^{2} d + a b^{4} c d^{2} - a^{2} b^{3} d^{3} - {\left(2 \, a^{3} b^{2} c^{2} d + 2 \, a^{3} b^{2} d^{3} - {\left(a^{2} b^{3} - b^{5}\right)} c^{3} - {\left(a^{4} b + 3 \, a^{2} b^{3}\right)} c d^{2}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} c^{2} d^{2} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{3} + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{4}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d + {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} c^{2} d^{2} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{3} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{4}\right)} f\right)}}"," ",0,"-1/2*(2*b^5*c^3 - 2*a*b^4*c^2*d + 2*b^5*c*d^2 - 2*a*b^4*d^3 + 2*(2*a^4*b*c^2*d + 2*a^4*b*d^3 - (a^3*b^2 - a*b^4)*c^3 - (a^5 + 3*a^3*b^2)*c*d^2)*f*x - (2*a^2*b^3*c^3 + 2*a^2*b^3*c*d^2 - (3*a^3*b^2 + a*b^4)*c^2*d - (3*a^3*b^2 + a*b^4)*d^3 + (2*a*b^4*c^3 + 2*a*b^4*c*d^2 - (3*a^2*b^3 + b^5)*c^2*d - (3*a^2*b^3 + b^5)*d^3)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - ((a^4*b + 2*a^2*b^3 + b^5)*d^3*tan(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*d^3)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(a*b^4*c^3 - a^2*b^3*c^2*d + a*b^4*c*d^2 - a^2*b^3*d^3 - (2*a^3*b^2*c^2*d + 2*a^3*b^2*d^3 - (a^2*b^3 - b^5)*c^3 - (a^4*b + 3*a^2*b^3)*c*d^2)*f*x)*tan(f*x + e))/(((a^4*b^3 + 2*a^2*b^5 + b^7)*c^4 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^3*d + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*c^2*d^2 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c*d^3 + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d^4)*f*tan(f*x + e) + ((a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^4 - 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c^3*d + (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*c^2*d^2 - 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c*d^3 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^4)*f)","B",0
1215,1,1927,0,2.006223," ","integrate(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(7 \, a^{2} b^{6} + b^{8}\right)} c^{4} - 4 \, {\left(4 \, a^{3} b^{5} + a b^{7}\right)} c^{3} d + {\left(9 \, a^{4} b^{4} + 10 \, a^{2} b^{6} + b^{8}\right)} c^{2} d^{2} - 4 \, {\left(4 \, a^{3} b^{5} + a b^{7}\right)} c d^{3} + 3 \, {\left(3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{4} - 2 \, {\left({\left(a^{5} b^{3} - 3 \, a^{3} b^{5}\right)} c^{4} - {\left(3 \, a^{6} b^{2} - 6 \, a^{4} b^{4} - a^{2} b^{6}\right)} c^{3} d + 3 \, {\left(a^{7} b - a^{3} b^{5}\right)} c^{2} d^{2} - {\left(a^{8} + 6 \, a^{6} b^{2} - 3 \, a^{4} b^{4}\right)} c d^{3} + {\left(3 \, a^{7} b - a^{5} b^{3}\right)} d^{4}\right)} f x + {\left(12 \, a^{3} b^{5} c^{3} d + 12 \, a^{3} b^{5} c d^{3} - {\left(5 \, a^{2} b^{6} - b^{8}\right)} c^{4} - {\left(7 \, a^{4} b^{4} + 6 \, a^{2} b^{6} - b^{8}\right)} c^{2} d^{2} - {\left(7 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{4} - 2 \, {\left({\left(a^{3} b^{5} - 3 \, a b^{7}\right)} c^{4} - {\left(3 \, a^{4} b^{4} - 6 \, a^{2} b^{6} - b^{8}\right)} c^{3} d + 3 \, {\left(a^{5} b^{3} - a b^{7}\right)} c^{2} d^{2} - {\left(a^{6} b^{2} + 6 \, a^{4} b^{4} - 3 \, a^{2} b^{6}\right)} c d^{3} + {\left(3 \, a^{5} b^{3} - a^{3} b^{5}\right)} d^{4}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(8 \, a^{5} b^{3} c^{3} d + 8 \, a^{5} b^{3} c d^{3} - {\left(3 \, a^{4} b^{4} - a^{2} b^{6}\right)} c^{4} - 6 \, {\left(a^{6} b^{2} + a^{4} b^{4}\right)} c^{2} d^{2} - {\left(6 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{4} + {\left(8 \, a^{3} b^{5} c^{3} d + 8 \, a^{3} b^{5} c d^{3} - {\left(3 \, a^{2} b^{6} - b^{8}\right)} c^{4} - 6 \, {\left(a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d^{2} - {\left(6 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{4}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(8 \, a^{4} b^{4} c^{3} d + 8 \, a^{4} b^{4} c d^{3} - {\left(3 \, a^{3} b^{5} - a b^{7}\right)} c^{4} - 6 \, {\left(a^{5} b^{3} + a^{3} b^{5}\right)} c^{2} d^{2} - {\left(6 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{4} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{4} \tan\left(f x + e\right) + {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{4}\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(3 \, {\left(a^{3} b^{5} - a b^{7}\right)} c^{4} - {\left(7 \, a^{4} b^{4} - 6 \, a^{2} b^{6} - b^{8}\right)} c^{3} d + 4 \, {\left(a^{5} b^{3} - a b^{7}\right)} c^{2} d^{2} - {\left(7 \, a^{4} b^{4} - 6 \, a^{2} b^{6} - b^{8}\right)} c d^{3} + {\left(4 \, a^{5} b^{3} - 3 \, a^{3} b^{5} - a b^{7}\right)} d^{4} + 2 \, {\left({\left(a^{4} b^{4} - 3 \, a^{2} b^{6}\right)} c^{4} - {\left(3 \, a^{5} b^{3} - 6 \, a^{3} b^{5} - a b^{7}\right)} c^{3} d + 3 \, {\left(a^{6} b^{2} - a^{2} b^{6}\right)} c^{2} d^{2} - {\left(a^{7} b + 6 \, a^{5} b^{3} - 3 \, a^{3} b^{5}\right)} c d^{3} + {\left(3 \, a^{6} b^{2} - a^{4} b^{4}\right)} d^{4}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} c^{5} - 3 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} c^{4} d + {\left(3 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 12 \, a^{4} b^{7} + 6 \, a^{2} b^{9} + b^{11}\right)} c^{3} d^{2} - {\left(a^{9} b^{2} + 6 \, a^{7} b^{4} + 12 \, a^{5} b^{6} + 10 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} d^{3} + 3 \, {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} c d^{4} - {\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} d^{5}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} c^{5} - 3 \, {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} c^{4} d + {\left(3 \, a^{9} b^{2} + 10 \, a^{7} b^{4} + 12 \, a^{5} b^{6} + 6 \, a^{3} b^{8} + a b^{10}\right)} c^{3} d^{2} - {\left(a^{10} b + 6 \, a^{8} b^{3} + 12 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 3 \, a^{2} b^{9}\right)} c^{2} d^{3} + 3 \, {\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} c d^{4} - {\left(a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}\right)} d^{5}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} c^{5} - 3 \, {\left(a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8}\right)} c^{4} d + {\left(3 \, a^{10} b + 10 \, a^{8} b^{3} + 12 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + a^{2} b^{9}\right)} c^{3} d^{2} - {\left(a^{11} + 6 \, a^{9} b^{2} + 12 \, a^{7} b^{4} + 10 \, a^{5} b^{6} + 3 \, a^{3} b^{8}\right)} c^{2} d^{3} + 3 \, {\left(a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}\right)} c d^{4} - {\left(a^{11} + 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} + a^{5} b^{6}\right)} d^{5}\right)} f\right)}}"," ",0,"-1/2*((7*a^2*b^6 + b^8)*c^4 - 4*(4*a^3*b^5 + a*b^7)*c^3*d + (9*a^4*b^4 + 10*a^2*b^6 + b^8)*c^2*d^2 - 4*(4*a^3*b^5 + a*b^7)*c*d^3 + 3*(3*a^4*b^4 + a^2*b^6)*d^4 - 2*((a^5*b^3 - 3*a^3*b^5)*c^4 - (3*a^6*b^2 - 6*a^4*b^4 - a^2*b^6)*c^3*d + 3*(a^7*b - a^3*b^5)*c^2*d^2 - (a^8 + 6*a^6*b^2 - 3*a^4*b^4)*c*d^3 + (3*a^7*b - a^5*b^3)*d^4)*f*x + (12*a^3*b^5*c^3*d + 12*a^3*b^5*c*d^3 - (5*a^2*b^6 - b^8)*c^4 - (7*a^4*b^4 + 6*a^2*b^6 - b^8)*c^2*d^2 - (7*a^4*b^4 + a^2*b^6)*d^4 - 2*((a^3*b^5 - 3*a*b^7)*c^4 - (3*a^4*b^4 - 6*a^2*b^6 - b^8)*c^3*d + 3*(a^5*b^3 - a*b^7)*c^2*d^2 - (a^6*b^2 + 6*a^4*b^4 - 3*a^2*b^6)*c*d^3 + (3*a^5*b^3 - a^3*b^5)*d^4)*f*x)*tan(f*x + e)^2 + (8*a^5*b^3*c^3*d + 8*a^5*b^3*c*d^3 - (3*a^4*b^4 - a^2*b^6)*c^4 - 6*(a^6*b^2 + a^4*b^4)*c^2*d^2 - (6*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^4 + (8*a^3*b^5*c^3*d + 8*a^3*b^5*c*d^3 - (3*a^2*b^6 - b^8)*c^4 - 6*(a^4*b^4 + a^2*b^6)*c^2*d^2 - (6*a^4*b^4 + 3*a^2*b^6 + b^8)*d^4)*tan(f*x + e)^2 + 2*(8*a^4*b^4*c^3*d + 8*a^4*b^4*c*d^3 - (3*a^3*b^5 - a*b^7)*c^4 - 6*(a^5*b^3 + a^3*b^5)*c^2*d^2 - (6*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^4)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + ((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^4*tan(f*x + e)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^4*tan(f*x + e) + (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*d^4)*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(3*(a^3*b^5 - a*b^7)*c^4 - (7*a^4*b^4 - 6*a^2*b^6 - b^8)*c^3*d + 4*(a^5*b^3 - a*b^7)*c^2*d^2 - (7*a^4*b^4 - 6*a^2*b^6 - b^8)*c*d^3 + (4*a^5*b^3 - 3*a^3*b^5 - a*b^7)*d^4 + 2*((a^4*b^4 - 3*a^2*b^6)*c^4 - (3*a^5*b^3 - 6*a^3*b^5 - a*b^7)*c^3*d + 3*(a^6*b^2 - a^2*b^6)*c^2*d^2 - (a^7*b + 6*a^5*b^3 - 3*a^3*b^5)*c*d^3 + (3*a^6*b^2 - a^4*b^4)*d^4)*f*x)*tan(f*x + e))/(((a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*c^5 - 3*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*c^4*d + (3*a^8*b^3 + 10*a^6*b^5 + 12*a^4*b^7 + 6*a^2*b^9 + b^11)*c^3*d^2 - (a^9*b^2 + 6*a^7*b^4 + 12*a^5*b^6 + 10*a^3*b^8 + 3*a*b^10)*c^2*d^3 + 3*(a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*c*d^4 - (a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*d^5)*f*tan(f*x + e)^2 + 2*((a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*c^5 - 3*(a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*c^4*d + (3*a^9*b^2 + 10*a^7*b^4 + 12*a^5*b^6 + 6*a^3*b^8 + a*b^10)*c^3*d^2 - (a^10*b + 6*a^8*b^3 + 12*a^6*b^5 + 10*a^4*b^7 + 3*a^2*b^9)*c^2*d^3 + 3*(a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*c*d^4 - (a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7)*d^5)*f*tan(f*x + e) + ((a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*c^5 - 3*(a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8)*c^4*d + (3*a^10*b + 10*a^8*b^3 + 12*a^6*b^5 + 6*a^4*b^7 + a^2*b^9)*c^3*d^2 - (a^11 + 6*a^9*b^2 + 12*a^7*b^4 + 10*a^5*b^6 + 3*a^3*b^8)*c^2*d^3 + 3*(a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7)*c*d^4 - (a^11 + 3*a^9*b^2 + 3*a^7*b^4 + a^5*b^6)*d^5)*f)","B",0
1216,1,704,0,1.062154," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{b^{4} c^{4} d^{2} - 4 \, a b^{3} c^{3} d^{3} + 6 \, a^{2} b^{2} c^{2} d^{4} - 4 \, a^{3} b c d^{5} + a^{4} d^{6} - {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{3} + 8 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{4} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{5}\right)} f x - {\left(b^{4} c^{4} d^{2} + 2 \, b^{4} c^{2} d^{4} + b^{4} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(b^{4} c^{6} - 2 \, a b^{3} c^{5} d + 2 \, b^{4} c^{4} d^{2} - 2 \, a^{3} b c d^{5} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} c^{3} d^{3} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c^{2} d^{4} + {\left(b^{4} c^{5} d - 2 \, a b^{3} c^{4} d^{2} + 2 \, b^{4} c^{3} d^{3} - 2 \, a^{3} b d^{6} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} c^{2} d^{4} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(b^{4} c^{6} - 2 \, a b^{3} c^{5} d + 2 \, b^{4} c^{4} d^{2} - 4 \, a b^{3} c^{3} d^{3} + b^{4} c^{2} d^{4} - 2 \, a b^{3} c d^{5} + {\left(b^{4} c^{5} d - 2 \, a b^{3} c^{4} d^{2} + 2 \, b^{4} c^{3} d^{3} - 4 \, a b^{3} c^{2} d^{4} + b^{4} c d^{5} - 2 \, a b^{3} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} - 4 \, a^{3} b c^{2} d^{4} + 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{3} + {\left(a^{4} + b^{4}\right)} c d^{5} + {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{4} + 8 \, {\left(a^{3} b - a b^{3}\right)} c d^{5} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d^{6}\right)} f x\right)} \tan\left(f x + e\right)}{{\left(c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right) + {\left(c^{5} d^{3} + 2 \, c^{3} d^{5} + c d^{7}\right)} f}"," ",0,"-(b^4*c^4*d^2 - 4*a*b^3*c^3*d^3 + 6*a^2*b^2*c^2*d^4 - 4*a^3*b*c*d^5 + a^4*d^6 - ((a^4 - 6*a^2*b^2 + b^4)*c^3*d^3 + 8*(a^3*b - a*b^3)*c^2*d^4 - (a^4 - 6*a^2*b^2 + b^4)*c*d^5)*f*x - (b^4*c^4*d^2 + 2*b^4*c^2*d^4 + b^4*d^6)*tan(f*x + e)^2 + (b^4*c^6 - 2*a*b^3*c^5*d + 2*b^4*c^4*d^2 - 2*a^3*b*c*d^5 + 2*(a^3*b - 3*a*b^3)*c^3*d^3 - (a^4 - 6*a^2*b^2)*c^2*d^4 + (b^4*c^5*d - 2*a*b^3*c^4*d^2 + 2*b^4*c^3*d^3 - 2*a^3*b*d^6 + 2*(a^3*b - 3*a*b^3)*c^2*d^4 - (a^4 - 6*a^2*b^2)*c*d^5)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (b^4*c^6 - 2*a*b^3*c^5*d + 2*b^4*c^4*d^2 - 4*a*b^3*c^3*d^3 + b^4*c^2*d^4 - 2*a*b^3*c*d^5 + (b^4*c^5*d - 2*a*b^3*c^4*d^2 + 2*b^4*c^3*d^3 - 4*a*b^3*c^2*d^4 + b^4*c*d^5 - 2*a*b^3*d^6)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - (2*b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 2*(3*a^2*b^2 + b^4)*c^3*d^3 + (a^4 + b^4)*c*d^5 + ((a^4 - 6*a^2*b^2 + b^4)*c^2*d^4 + 8*(a^3*b - a*b^3)*c*d^5 - (a^4 - 6*a^2*b^2 + b^4)*d^6)*f*x)*tan(f*x + e))/((c^4*d^4 + 2*c^2*d^6 + d^8)*f*tan(f*x + e) + (c^5*d^3 + 2*c^3*d^5 + c*d^7)*f)","B",0
1217,1,492,0,0.634056," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} c^{3} d^{2} - 6 \, a b^{2} c^{2} d^{3} + 6 \, a^{2} b c d^{4} - 2 \, a^{3} d^{5} + 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{3} d^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d^{3} - {\left(a^{3} - 3 \, a b^{2}\right)} c d^{4}\right)} f x + {\left(b^{3} c^{5} + 3 \, a^{2} b c d^{4} - 3 \, {\left(a^{2} b - b^{3}\right)} c^{3} d^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d^{3} + {\left(b^{3} c^{4} d + 3 \, a^{2} b d^{5} - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(b^{3} c^{5} + 2 \, b^{3} c^{3} d^{2} + b^{3} c d^{4} + {\left(b^{3} c^{4} d + 2 \, b^{3} c^{2} d^{3} + b^{3} d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4} - {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d^{3} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{4} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{5}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{3} d^{4} + c d^{6}\right)} f\right)}}"," ",0,"1/2*(2*b^3*c^3*d^2 - 6*a*b^2*c^2*d^3 + 6*a^2*b*c*d^4 - 2*a^3*d^5 + 2*((a^3 - 3*a*b^2)*c^3*d^2 + 2*(3*a^2*b - b^3)*c^2*d^3 - (a^3 - 3*a*b^2)*c*d^4)*f*x + (b^3*c^5 + 3*a^2*b*c*d^4 - 3*(a^2*b - b^3)*c^3*d^2 + 2*(a^3 - 3*a*b^2)*c^2*d^3 + (b^3*c^4*d + 3*a^2*b*d^5 - 3*(a^2*b - b^3)*c^2*d^3 + 2*(a^3 - 3*a*b^2)*c*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (b^3*c^5 + 2*b^3*c^3*d^2 + b^3*c*d^4 + (b^3*c^4*d + 2*b^3*c^2*d^3 + b^3*d^5)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4 - ((a^3 - 3*a*b^2)*c^2*d^3 + 2*(3*a^2*b - b^3)*c*d^4 - (a^3 - 3*a*b^2)*d^5)*f*x)*tan(f*x + e))/((c^4*d^3 + 2*c^2*d^5 + d^7)*f*tan(f*x + e) + (c^5*d^2 + 2*c^3*d^4 + c*d^6)*f)","B",0
1218,1,294,0,0.646288," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3} - {\left(4 \, a b c^{2} d + {\left(a^{2} - b^{2}\right)} c^{3} - {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f x + {\left(a b c^{3} - a b c d^{2} - {\left(a^{2} - b^{2}\right)} c^{2} d + {\left(a b c^{2} d - a b d^{3} - {\left(a^{2} - b^{2}\right)} c d^{2}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(4 \, a b c d^{2} + {\left(a^{2} - b^{2}\right)} c^{2} d - {\left(a^{2} - b^{2}\right)} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{{\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} f \tan\left(f x + e\right) + {\left(c^{5} + 2 \, c^{3} d^{2} + c d^{4}\right)} f}"," ",0,"-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3 - (4*a*b*c^2*d + (a^2 - b^2)*c^3 - (a^2 - b^2)*c*d^2)*f*x + (a*b*c^3 - a*b*c*d^2 - (a^2 - b^2)*c^2*d + (a*b*c^2*d - a*b*d^3 - (a^2 - b^2)*c*d^2)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (4*a*b*c*d^2 + (a^2 - b^2)*c^2*d - (a^2 - b^2)*d^3)*f*x)*tan(f*x + e))/((c^4*d + 2*c^2*d^3 + d^5)*f*tan(f*x + e) + (c^5 + 2*c^3*d^2 + c*d^4)*f)","B",0
1219,1,222,0,0.507758," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, b c d^{2} - 2 \, a d^{3} + 2 \, {\left(a c^{3} + 2 \, b c^{2} d - a c d^{2}\right)} f x - {\left(b c^{3} - 2 \, a c^{2} d - b c d^{2} + {\left(b c^{2} d - 2 \, a c d^{2} - b d^{3}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b c^{2} d - a c d^{2} - {\left(a c^{2} d + 2 \, b c d^{2} - a d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} f \tan\left(f x + e\right) + {\left(c^{5} + 2 \, c^{3} d^{2} + c d^{4}\right)} f\right)}}"," ",0,"1/2*(2*b*c*d^2 - 2*a*d^3 + 2*(a*c^3 + 2*b*c^2*d - a*c*d^2)*f*x - (b*c^3 - 2*a*c^2*d - b*c*d^2 + (b*c^2*d - 2*a*c*d^2 - b*d^3)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(b*c^2*d - a*c*d^2 - (a*c^2*d + 2*b*c*d^2 - a*d^3)*f*x)*tan(f*x + e))/((c^4*d + 2*c^2*d^3 + d^5)*f*tan(f*x + e) + (c^5 + 2*c^3*d^2 + c*d^4)*f)","A",0
1220,1,711,0,1.060121," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b + b^{3}\right)} c d^{4} - 2 \, {\left(a^{3} + a b^{2}\right)} d^{5} + 2 \, {\left(a b^{2} c^{5} - a^{3} c d^{4} - 2 \, {\left(a^{2} b + b^{3}\right)} c^{4} d + {\left(a^{3} + 3 \, a b^{2}\right)} c^{3} d^{2}\right)} f x + {\left(b^{3} c^{5} + 2 \, b^{3} c^{3} d^{2} + b^{3} c d^{4} + {\left(b^{3} c^{4} d + 2 \, b^{3} c^{2} d^{3} + b^{3} d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(3 \, {\left(a^{2} b + b^{3}\right)} c^{3} d^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{3} + {\left(a^{2} b + b^{3}\right)} c d^{4} + {\left(3 \, {\left(a^{2} b + b^{3}\right)} c^{2} d^{3} - 2 \, {\left(a^{3} + a b^{2}\right)} c d^{4} + {\left(a^{2} b + b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} d^{3} - {\left(a^{3} + a b^{2}\right)} c d^{4} - {\left(a b^{2} c^{4} d - a^{3} d^{5} - 2 \, {\left(a^{2} b + b^{3}\right)} c^{3} d^{2} + {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{2} + b^{4}\right)} c^{6} d - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{5} d^{2} + {\left(a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{3} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{3} d^{4} + {\left(2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{5} - 2 \, {\left(a^{3} b + a b^{3}\right)} c d^{6} + {\left(a^{4} + a^{2} b^{2}\right)} d^{7}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{2} b^{2} + b^{4}\right)} c^{7} - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{6} d + {\left(a^{4} + 3 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{5} d^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{4} d^{3} + {\left(2 \, a^{4} + 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d^{5} + {\left(a^{4} + a^{2} b^{2}\right)} c d^{6}\right)} f\right)}}"," ",0,"1/2*(2*(a^2*b + b^3)*c*d^4 - 2*(a^3 + a*b^2)*d^5 + 2*(a*b^2*c^5 - a^3*c*d^4 - 2*(a^2*b + b^3)*c^4*d + (a^3 + 3*a*b^2)*c^3*d^2)*f*x + (b^3*c^5 + 2*b^3*c^3*d^2 + b^3*c*d^4 + (b^3*c^4*d + 2*b^3*c^2*d^3 + b^3*d^5)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (3*(a^2*b + b^3)*c^3*d^2 - 2*(a^3 + a*b^2)*c^2*d^3 + (a^2*b + b^3)*c*d^4 + (3*(a^2*b + b^3)*c^2*d^3 - 2*(a^3 + a*b^2)*c*d^4 + (a^2*b + b^3)*d^5)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*((a^2*b + b^3)*c^2*d^3 - (a^3 + a*b^2)*c*d^4 - (a*b^2*c^4*d - a^3*d^5 - 2*(a^2*b + b^3)*c^3*d^2 + (a^3 + 3*a*b^2)*c^2*d^3)*f*x)*tan(f*x + e))/(((a^2*b^2 + b^4)*c^6*d - 2*(a^3*b + a*b^3)*c^5*d^2 + (a^4 + 3*a^2*b^2 + 2*b^4)*c^4*d^3 - 4*(a^3*b + a*b^3)*c^3*d^4 + (2*a^4 + 3*a^2*b^2 + b^4)*c^2*d^5 - 2*(a^3*b + a*b^3)*c*d^6 + (a^4 + a^2*b^2)*d^7)*f*tan(f*x + e) + ((a^2*b^2 + b^4)*c^7 - 2*(a^3*b + a*b^3)*c^6*d + (a^4 + 3*a^2*b^2 + 2*b^4)*c^5*d^2 - 4*(a^3*b + a*b^3)*c^4*d^3 + (2*a^4 + 3*a^2*b^2 + b^4)*c^3*d^4 - 2*(a^3*b + a*b^3)*c^2*d^5 + (a^4 + a^2*b^2)*c*d^6)*f)","B",0
1221,1,2217,0,2.069511," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{b^{6} c^{6} - a b^{5} c^{5} d + 2 \, b^{6} c^{4} d^{2} - 2 \, a b^{5} c^{3} d^{3} + b^{6} c^{2} d^{4} + {\left(a^{5} b + 2 \, a^{3} b^{3}\right)} c d^{5} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{6} - {\left({\left(a^{3} b^{3} - a b^{5}\right)} c^{6} - {\left(3 \, a^{4} b^{2} + a^{2} b^{4}\right)} c^{5} d + {\left(3 \, a^{5} b + 8 \, a^{3} b^{3} + a b^{5}\right)} c^{4} d^{2} - {\left(a^{6} + 8 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} c^{3} d^{3} + {\left(a^{5} b + 3 \, a^{3} b^{3}\right)} c^{2} d^{4} + {\left(a^{6} - a^{4} b^{2}\right)} c d^{5}\right)} f x - {\left(a b^{5} c^{5} d - a^{2} b^{4} c^{4} d^{2} + 2 \, a b^{5} c^{3} d^{3} - a^{2} b^{4} d^{6} + {\left(a^{4} b^{2} + b^{6}\right)} c^{2} d^{4} - {\left(a^{5} b + 2 \, a^{3} b^{3}\right)} c d^{5} + {\left({\left(a^{2} b^{4} - b^{6}\right)} c^{5} d - {\left(3 \, a^{3} b^{3} + a b^{5}\right)} c^{4} d^{2} + {\left(3 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + b^{6}\right)} c^{3} d^{3} - {\left(a^{5} b + 8 \, a^{3} b^{3} + 3 \, a b^{5}\right)} c^{2} d^{4} + {\left(a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} c d^{5} + {\left(a^{5} b - a^{3} b^{3}\right)} d^{6}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left(a^{2} b^{4} c^{6} + 2 \, a^{2} b^{4} c^{4} d^{2} + a^{2} b^{4} c^{2} d^{4} - {\left(2 \, a^{3} b^{3} + a b^{5}\right)} c^{5} d - 2 \, {\left(2 \, a^{3} b^{3} + a b^{5}\right)} c^{3} d^{3} - {\left(2 \, a^{3} b^{3} + a b^{5}\right)} c d^{5} + {\left(a b^{5} c^{5} d + 2 \, a b^{5} c^{3} d^{3} + a b^{5} c d^{5} - {\left(2 \, a^{2} b^{4} + b^{6}\right)} c^{4} d^{2} - 2 \, {\left(2 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{4} - {\left(2 \, a^{2} b^{4} + b^{6}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(a b^{5} c^{6} - {\left(a^{2} b^{4} + b^{6}\right)} c^{5} d - {\left(2 \, a^{3} b^{3} - a b^{5}\right)} c^{4} d^{2} - 2 \, {\left(a^{2} b^{4} + b^{6}\right)} c^{3} d^{3} - {\left(4 \, a^{3} b^{3} + a b^{5}\right)} c^{2} d^{4} - {\left(a^{2} b^{4} + b^{6}\right)} c d^{5} - {\left(2 \, a^{3} b^{3} + a b^{5}\right)} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c^{3} d^{3} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} c^{2} d^{4} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c d^{5} + {\left(2 \, {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{4} - {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c d^{5} + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} c^{3} d^{3} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c^{2} d^{4} - {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} c d^{5} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{6}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(a b^{5} c^{6} + 3 \, a b^{5} c^{4} d^{2} - {\left(a^{2} b^{4} + b^{6}\right)} c^{5} d - 2 \, {\left(a^{2} b^{4} + b^{6}\right)} c^{3} d^{3} + {\left(a^{5} b + 2 \, a^{3} b^{3} + 4 \, a b^{5}\right)} c^{2} d^{4} - {\left(a^{6} + 3 \, a^{4} b^{2} + 4 \, a^{2} b^{4} + 2 \, b^{6}\right)} c d^{5} + {\left(a^{5} b + 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} d^{6} + {\left({\left(a^{2} b^{4} - b^{6}\right)} c^{6} - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{5} d + {\left(7 \, a^{2} b^{4} + b^{6}\right)} c^{4} d^{2} + 2 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d^{3} - {\left(a^{6} + 7 \, a^{4} b^{2}\right)} c^{2} d^{4} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} c d^{5} + {\left(a^{6} - a^{4} b^{2}\right)} d^{6}\right)} f x\right)} \tan\left(f x + e\right)}{{\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{7} d - 3 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{6} d^{2} + {\left(3 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 7 \, a^{2} b^{6} + 2 \, b^{8}\right)} c^{5} d^{3} - {\left(a^{7} b + 8 \, a^{5} b^{3} + 13 \, a^{3} b^{5} + 6 \, a b^{7}\right)} c^{4} d^{4} + {\left(6 \, a^{6} b^{2} + 13 \, a^{4} b^{4} + 8 \, a^{2} b^{6} + b^{8}\right)} c^{3} d^{5} - {\left(2 \, a^{7} b + 7 \, a^{5} b^{3} + 8 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} d^{6} + 3 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c d^{7} - {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d^{8}\right)} f \tan\left(f x + e\right)^{2} + {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{8} - 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{7} d + 2 \, {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{6} d^{2} + 2 \, {\left(a^{7} b - 3 \, a^{3} b^{5} - 2 \, a b^{7}\right)} c^{5} d^{3} - {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{4} d^{4} + 2 \, {\left(2 \, a^{7} b + 3 \, a^{5} b^{3} - a b^{7}\right)} c^{3} d^{5} - 2 \, {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} c^{2} d^{6} + 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c d^{7} - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d^{8}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{8} - 3 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{7} d + {\left(3 \, a^{7} b + 8 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + 2 \, a b^{7}\right)} c^{6} d^{2} - {\left(a^{8} + 8 \, a^{6} b^{2} + 13 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} c^{5} d^{3} + {\left(6 \, a^{7} b + 13 \, a^{5} b^{3} + 8 \, a^{3} b^{5} + a b^{7}\right)} c^{4} d^{4} - {\left(2 \, a^{8} + 7 \, a^{6} b^{2} + 8 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} c^{3} d^{5} + 3 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c^{2} d^{6} - {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} c d^{7}\right)} f}"," ",0,"-(b^6*c^6 - a*b^5*c^5*d + 2*b^6*c^4*d^2 - 2*a*b^5*c^3*d^3 + b^6*c^2*d^4 + (a^5*b + 2*a^3*b^3)*c*d^5 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d^6 - ((a^3*b^3 - a*b^5)*c^6 - (3*a^4*b^2 + a^2*b^4)*c^5*d + (3*a^5*b + 8*a^3*b^3 + a*b^5)*c^4*d^2 - (a^6 + 8*a^4*b^2 + 3*a^2*b^4)*c^3*d^3 + (a^5*b + 3*a^3*b^3)*c^2*d^4 + (a^6 - a^4*b^2)*c*d^5)*f*x - (a*b^5*c^5*d - a^2*b^4*c^4*d^2 + 2*a*b^5*c^3*d^3 - a^2*b^4*d^6 + (a^4*b^2 + b^6)*c^2*d^4 - (a^5*b + 2*a^3*b^3)*c*d^5 + ((a^2*b^4 - b^6)*c^5*d - (3*a^3*b^3 + a*b^5)*c^4*d^2 + (3*a^4*b^2 + 8*a^2*b^4 + b^6)*c^3*d^3 - (a^5*b + 8*a^3*b^3 + 3*a*b^5)*c^2*d^4 + (a^4*b^2 + 3*a^2*b^4)*c*d^5 + (a^5*b - a^3*b^3)*d^6)*f*x)*tan(f*x + e)^2 - (a^2*b^4*c^6 + 2*a^2*b^4*c^4*d^2 + a^2*b^4*c^2*d^4 - (2*a^3*b^3 + a*b^5)*c^5*d - 2*(2*a^3*b^3 + a*b^5)*c^3*d^3 - (2*a^3*b^3 + a*b^5)*c*d^5 + (a*b^5*c^5*d + 2*a*b^5*c^3*d^3 + a*b^5*c*d^5 - (2*a^2*b^4 + b^6)*c^4*d^2 - 2*(2*a^2*b^4 + b^6)*c^2*d^4 - (2*a^2*b^4 + b^6)*d^6)*tan(f*x + e)^2 + (a*b^5*c^6 - (a^2*b^4 + b^6)*c^5*d - (2*a^3*b^3 - a*b^5)*c^4*d^2 - 2*(a^2*b^4 + b^6)*c^3*d^3 - (4*a^3*b^3 + a*b^5)*c^2*d^4 - (a^2*b^4 + b^6)*c*d^5 - (2*a^3*b^3 + a*b^5)*d^6)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (2*(a^5*b + 2*a^3*b^3 + a*b^5)*c^3*d^3 - (a^6 + 2*a^4*b^2 + a^2*b^4)*c^2*d^4 + (a^5*b + 2*a^3*b^3 + a*b^5)*c*d^5 + (2*(a^4*b^2 + 2*a^2*b^4 + b^6)*c^2*d^4 - (a^5*b + 2*a^3*b^3 + a*b^5)*c*d^5 + (a^4*b^2 + 2*a^2*b^4 + b^6)*d^6)*tan(f*x + e)^2 + (2*(a^4*b^2 + 2*a^2*b^4 + b^6)*c^3*d^3 + (a^5*b + 2*a^3*b^3 + a*b^5)*c^2*d^4 - (a^6 + a^4*b^2 - a^2*b^4 - b^6)*c*d^5 + (a^5*b + 2*a^3*b^3 + a*b^5)*d^6)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (a*b^5*c^6 + 3*a*b^5*c^4*d^2 - (a^2*b^4 + b^6)*c^5*d - 2*(a^2*b^4 + b^6)*c^3*d^3 + (a^5*b + 2*a^3*b^3 + 4*a*b^5)*c^2*d^4 - (a^6 + 3*a^4*b^2 + 4*a^2*b^4 + 2*b^6)*c*d^5 + (a^5*b + 2*a^3*b^3 + 2*a*b^5)*d^6 + ((a^2*b^4 - b^6)*c^6 - 2*(a^3*b^3 + a*b^5)*c^5*d + (7*a^2*b^4 + b^6)*c^4*d^2 + 2*(a^5*b - a*b^5)*c^3*d^3 - (a^6 + 7*a^4*b^2)*c^2*d^4 + 2*(a^5*b + a^3*b^3)*c*d^5 + (a^6 - a^4*b^2)*d^6)*f*x)*tan(f*x + e))/(((a^4*b^4 + 2*a^2*b^6 + b^8)*c^7*d - 3*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^6*d^2 + (3*a^6*b^2 + 8*a^4*b^4 + 7*a^2*b^6 + 2*b^8)*c^5*d^3 - (a^7*b + 8*a^5*b^3 + 13*a^3*b^5 + 6*a*b^7)*c^4*d^4 + (6*a^6*b^2 + 13*a^4*b^4 + 8*a^2*b^6 + b^8)*c^3*d^5 - (2*a^7*b + 7*a^5*b^3 + 8*a^3*b^5 + 3*a*b^7)*c^2*d^6 + 3*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c*d^7 - (a^7*b + 2*a^5*b^3 + a^3*b^5)*d^8)*f*tan(f*x + e)^2 + ((a^4*b^4 + 2*a^2*b^6 + b^8)*c^8 - 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^7*d + 2*(a^4*b^4 + 2*a^2*b^6 + b^8)*c^6*d^2 + 2*(a^7*b - 3*a^3*b^5 - 2*a*b^7)*c^5*d^3 - (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^4*d^4 + 2*(2*a^7*b + 3*a^5*b^3 - a*b^7)*c^3*d^5 - 2*(a^8 + 2*a^6*b^2 + a^4*b^4)*c^2*d^6 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d^7 - (a^8 + 2*a^6*b^2 + a^4*b^4)*d^8)*f*tan(f*x + e) + ((a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^8 - 3*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^7*d + (3*a^7*b + 8*a^5*b^3 + 7*a^3*b^5 + 2*a*b^7)*c^6*d^2 - (a^8 + 8*a^6*b^2 + 13*a^4*b^4 + 6*a^2*b^6)*c^5*d^3 + (6*a^7*b + 13*a^5*b^3 + 8*a^3*b^5 + a*b^7)*c^4*d^4 - (2*a^8 + 7*a^6*b^2 + 8*a^4*b^4 + 3*a^2*b^6)*c^3*d^5 + 3*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c^2*d^6 - (a^8 + 2*a^6*b^2 + a^4*b^4)*c*d^7)*f)","B",0
1222,1,4749,0,4.653933," ","integrate(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(7 \, a^{2} b^{7} + b^{9}\right)} c^{7} - 6 \, {\left(3 \, a^{3} b^{6} + a b^{8}\right)} c^{6} d + {\left(11 \, a^{4} b^{5} + 19 \, a^{2} b^{7} + 2 \, b^{9}\right)} c^{5} d^{2} - 12 \, {\left(3 \, a^{3} b^{6} + a b^{8}\right)} c^{4} d^{3} + {\left(22 \, a^{4} b^{5} + 17 \, a^{2} b^{7} + b^{9}\right)} c^{3} d^{4} - 6 \, {\left(3 \, a^{3} b^{6} + a b^{8}\right)} c^{2} d^{5} - {\left(2 \, a^{8} b + 6 \, a^{6} b^{3} - 5 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} c d^{6} + 2 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{7} - {\left({\left(5 \, a^{2} b^{7} - b^{9}\right)} c^{6} d - 2 \, {\left(7 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d^{2} + {\left(9 \, a^{4} b^{5} + 13 \, a^{2} b^{7} - 2 \, b^{9}\right)} c^{4} d^{3} - 4 \, {\left(7 \, a^{3} b^{6} + a b^{8}\right)} c^{3} d^{4} - {\left(2 \, a^{6} b^{3} - 12 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + 3 \, b^{9}\right)} c^{2} d^{5} + 2 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} - 4 \, a^{3} b^{6}\right)} c d^{6} + 3 \, {\left(3 \, a^{4} b^{5} + a^{2} b^{7}\right)} d^{7} + 2 \, {\left({\left(a^{3} b^{6} - 3 \, a b^{8}\right)} c^{6} d - 2 \, {\left(2 \, a^{4} b^{5} - 3 \, a^{2} b^{7} - b^{9}\right)} c^{5} d^{2} + {\left(6 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 5 \, a b^{8}\right)} c^{4} d^{3} - 4 \, {\left(a^{6} b^{3} + 5 \, a^{4} b^{5}\right)} c^{3} d^{4} + {\left(a^{7} b^{2} + 15 \, a^{5} b^{4} + 10 \, a^{3} b^{6}\right)} c^{2} d^{5} - 2 \, {\left(a^{6} b^{3} + 5 \, a^{4} b^{5}\right)} c d^{6} - {\left(a^{7} b^{2} - 3 \, a^{5} b^{4}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)^{3} - 2 \, {\left({\left(a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} c^{7} - 2 \, {\left(2 \, a^{6} b^{3} - 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} c^{6} d + {\left(6 \, a^{7} b^{2} + 5 \, a^{5} b^{4} - 5 \, a^{3} b^{6}\right)} c^{5} d^{2} - 4 \, {\left(a^{8} b + 5 \, a^{6} b^{3}\right)} c^{4} d^{3} + {\left(a^{9} + 15 \, a^{7} b^{2} + 10 \, a^{5} b^{4}\right)} c^{3} d^{4} - 2 \, {\left(a^{8} b + 5 \, a^{6} b^{3}\right)} c^{2} d^{5} - {\left(a^{9} - 3 \, a^{7} b^{2}\right)} c d^{6}\right)} f x - {\left({\left(5 \, a^{2} b^{7} - b^{9}\right)} c^{7} - 8 \, {\left(a^{3} b^{6} + a b^{8}\right)} c^{6} d - {\left(7 \, a^{4} b^{5} - 25 \, a^{2} b^{7} - 2 \, b^{9}\right)} c^{5} d^{2} + 2 \, {\left(5 \, a^{5} b^{4} - 11 \, a^{3} b^{6} - 10 \, a b^{8}\right)} c^{4} d^{3} - 7 \, {\left(2 \, a^{4} b^{5} - 5 \, a^{2} b^{7} - b^{9}\right)} c^{3} d^{4} - 4 \, {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + 8 \, a^{3} b^{6} + 5 \, a b^{8}\right)} c^{2} d^{5} + {\left(4 \, a^{8} b + 14 \, a^{6} b^{3} + 11 \, a^{4} b^{5} + 25 \, a^{2} b^{7} + 6 \, b^{9}\right)} c d^{6} - 2 \, {\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + 6 \, a^{3} b^{6} + 3 \, a b^{8}\right)} d^{7} + 2 \, {\left({\left(a^{3} b^{6} - 3 \, a b^{8}\right)} c^{7} - 2 \, {\left(a^{4} b^{5} - b^{9}\right)} c^{6} d - {\left(2 \, a^{5} b^{4} - 17 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d^{2} + 2 \, {\left(4 \, a^{6} b^{3} - 5 \, a^{4} b^{5} - 5 \, a^{2} b^{7}\right)} c^{4} d^{3} - {\left(7 \, a^{7} b^{2} + 25 \, a^{5} b^{4} - 10 \, a^{3} b^{6}\right)} c^{3} d^{4} + 2 \, {\left(a^{8} b + 14 \, a^{6} b^{3} + 5 \, a^{4} b^{5}\right)} c^{2} d^{5} - {\left(5 \, a^{7} b^{2} + 17 \, a^{5} b^{4}\right)} c d^{6} - 2 \, {\left(a^{8} b - 3 \, a^{6} b^{3}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left({\left(3 \, a^{4} b^{5} - a^{2} b^{7}\right)} c^{7} - 2 \, {\left(5 \, a^{5} b^{4} + a^{3} b^{6}\right)} c^{6} d + {\left(10 \, a^{6} b^{3} + 15 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{5} d^{2} - 4 \, {\left(5 \, a^{5} b^{4} + a^{3} b^{6}\right)} c^{4} d^{3} + {\left(20 \, a^{6} b^{3} + 21 \, a^{4} b^{5} + 5 \, a^{2} b^{7}\right)} c^{3} d^{4} - 2 \, {\left(5 \, a^{5} b^{4} + a^{3} b^{6}\right)} c^{2} d^{5} + {\left(10 \, a^{6} b^{3} + 9 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} c d^{6} + {\left({\left(3 \, a^{2} b^{7} - b^{9}\right)} c^{6} d - 2 \, {\left(5 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d^{2} + {\left(10 \, a^{4} b^{5} + 15 \, a^{2} b^{7} + b^{9}\right)} c^{4} d^{3} - 4 \, {\left(5 \, a^{3} b^{6} + a b^{8}\right)} c^{3} d^{4} + {\left(20 \, a^{4} b^{5} + 21 \, a^{2} b^{7} + 5 \, b^{9}\right)} c^{2} d^{5} - 2 \, {\left(5 \, a^{3} b^{6} + a b^{8}\right)} c d^{6} + {\left(10 \, a^{4} b^{5} + 9 \, a^{2} b^{7} + 3 \, b^{9}\right)} d^{7}\right)} \tan\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b^{7} - b^{9}\right)} c^{7} - 4 \, {\left(a^{3} b^{6} + a b^{8}\right)} c^{6} d - {\left(10 \, a^{4} b^{5} - 11 \, a^{2} b^{7} - b^{9}\right)} c^{5} d^{2} + 2 \, {\left(10 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - a b^{8}\right)} c^{4} d^{3} - {\left(20 \, a^{4} b^{5} - 13 \, a^{2} b^{7} - 5 \, b^{9}\right)} c^{3} d^{4} + 8 \, {\left(5 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} c^{2} d^{5} - {\left(10 \, a^{4} b^{5} - 5 \, a^{2} b^{7} - 3 \, b^{9}\right)} c d^{6} + 2 \, {\left(10 \, a^{5} b^{4} + 9 \, a^{3} b^{6} + 3 \, a b^{8}\right)} d^{7}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(3 \, a^{3} b^{6} - a b^{8}\right)} c^{7} - {\left(17 \, a^{4} b^{5} + 5 \, a^{2} b^{7}\right)} c^{6} d + 2 \, {\left(5 \, a^{5} b^{4} + 14 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d^{2} + {\left(10 \, a^{6} b^{3} - 25 \, a^{4} b^{5} - 7 \, a^{2} b^{7}\right)} c^{4} d^{3} + 2 \, {\left(10 \, a^{5} b^{4} + 19 \, a^{3} b^{6} + 5 \, a b^{8}\right)} c^{3} d^{4} + {\left(20 \, a^{6} b^{3} + a^{4} b^{5} + a^{2} b^{7}\right)} c^{2} d^{5} + 2 \, {\left(5 \, a^{5} b^{4} + 8 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c d^{6} + {\left(10 \, a^{6} b^{3} + 9 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + {\left(5 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{3} d^{4} - 2 \, {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} c^{2} d^{5} + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c d^{6} + {\left(5 \, {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} c^{2} d^{5} - 2 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c d^{6} + 3 \, {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} d^{7}\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} c^{3} d^{4} + 8 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c^{2} d^{5} - {\left(4 \, a^{8} b + 9 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - 5 \, a^{2} b^{7} - 3 \, b^{9}\right)} c d^{6} + 6 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} d^{7}\right)} \tan\left(f x + e\right)^{2} + {\left(10 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c^{3} d^{4} + {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{2} d^{5} - 2 \, {\left(a^{9} - 6 \, a^{5} b^{4} - 8 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c d^{6} + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(6 \, {\left(a^{3} b^{6} - a b^{8}\right)} c^{7} - {\left(16 \, a^{4} b^{5} - 5 \, a^{2} b^{7} - 3 \, b^{9}\right)} c^{6} d + 2 \, {\left(5 \, a^{5} b^{4} + 12 \, a^{3} b^{6} - 5 \, a b^{8}\right)} c^{5} d^{2} - {\left(43 \, a^{4} b^{5} - 5 \, a^{2} b^{7} - 6 \, b^{9}\right)} c^{4} d^{3} + 2 \, {\left(10 \, a^{5} b^{4} + 15 \, a^{3} b^{6} - a b^{8}\right)} c^{3} d^{4} - {\left(2 \, a^{8} b + 6 \, a^{6} b^{3} + 44 \, a^{4} b^{5} + 7 \, a^{2} b^{7} - 3 \, b^{9}\right)} c^{2} d^{5} + 2 \, {\left(a^{9} + 5 \, a^{7} b^{2} + 14 \, a^{5} b^{4} + 13 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c d^{6} - {\left(4 \, a^{8} b + 12 \, a^{6} b^{3} + 23 \, a^{4} b^{5} + 9 \, a^{2} b^{7}\right)} d^{7} + 2 \, {\left(2 \, {\left(a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} c^{7} - {\left(7 \, a^{5} b^{4} - 9 \, a^{3} b^{6} - 4 \, a b^{8}\right)} c^{6} d + 8 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} - a^{2} b^{7}\right)} c^{5} d^{2} - {\left(2 \, a^{7} b^{2} + 35 \, a^{5} b^{4} + 5 \, a^{3} b^{6}\right)} c^{4} d^{3} - 2 \, {\left(a^{8} b - 5 \, a^{6} b^{3} - 10 \, a^{4} b^{5}\right)} c^{3} d^{4} + {\left(a^{9} + 11 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{2} d^{5} - 4 \, {\left(a^{8} b + a^{6} b^{3}\right)} c d^{6} - {\left(a^{9} - 3 \, a^{7} b^{2}\right)} d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} c^{8} d - 4 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} c^{7} d^{2} + 2 \, {\left(3 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 12 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{6} d^{3} - 4 \, {\left(a^{9} b^{3} + 5 \, a^{7} b^{5} + 9 \, a^{5} b^{7} + 7 \, a^{3} b^{9} + 2 \, a b^{11}\right)} c^{5} d^{4} + {\left(a^{10} b^{2} + 15 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 40 \, a^{4} b^{8} + 15 \, a^{2} b^{10} + b^{12}\right)} c^{4} d^{5} - 4 \, {\left(2 \, a^{9} b^{3} + 7 \, a^{7} b^{5} + 9 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} c^{3} d^{6} + 2 \, {\left(a^{10} b^{2} + 6 \, a^{8} b^{4} + 12 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 3 \, a^{2} b^{10}\right)} c^{2} d^{7} - 4 \, {\left(a^{9} b^{3} + 3 \, a^{7} b^{5} + 3 \, a^{5} b^{7} + a^{3} b^{9}\right)} c d^{8} + {\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} d^{9}\right)} f \tan\left(f x + e\right)^{3} + {\left({\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} c^{9} - 2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} c^{8} d - 2 \, {\left(a^{8} b^{4} + 2 \, a^{6} b^{6} - 2 \, a^{2} b^{10} - b^{12}\right)} c^{7} d^{2} + 4 \, {\left(2 \, a^{9} b^{3} + 5 \, a^{7} b^{5} + 3 \, a^{5} b^{7} - a^{3} b^{9} - a b^{11}\right)} c^{6} d^{3} - {\left(7 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 32 \, a^{6} b^{6} + 16 \, a^{4} b^{8} + a^{2} b^{10} - b^{12}\right)} c^{5} d^{4} + 2 \, {\left(a^{11} b + 11 \, a^{9} b^{3} + 26 \, a^{7} b^{5} + 22 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c^{4} d^{5} - 2 \, {\left(7 \, a^{10} b^{2} + 22 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{3} d^{6} + 4 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 9 \, a^{7} b^{5} + 7 \, a^{5} b^{7} + 2 \, a^{3} b^{9}\right)} c^{2} d^{7} - 7 \, {\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} c d^{8} + 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} d^{9}\right)} f \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} c^{9} - 7 \, {\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{8} d + 4 \, {\left(2 \, a^{9} b^{3} + 7 \, a^{7} b^{5} + 9 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} c^{7} d^{2} - 2 \, {\left(a^{10} b^{2} + 10 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 22 \, a^{4} b^{8} + 7 \, a^{2} b^{10}\right)} c^{6} d^{3} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 22 \, a^{7} b^{5} - 26 \, a^{5} b^{7} - 11 \, a^{3} b^{9} - a b^{11}\right)} c^{5} d^{4} + {\left(a^{12} - a^{10} b^{2} - 16 \, a^{8} b^{4} - 32 \, a^{6} b^{6} - 25 \, a^{4} b^{8} - 7 \, a^{2} b^{10}\right)} c^{4} d^{5} - 4 \, {\left(a^{11} b + a^{9} b^{3} - 3 \, a^{7} b^{5} - 5 \, a^{5} b^{7} - 2 \, a^{3} b^{9}\right)} c^{3} d^{6} + 2 \, {\left(a^{12} + 2 \, a^{10} b^{2} - 2 \, a^{6} b^{6} - a^{4} b^{8}\right)} c^{2} d^{7} - 2 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} c d^{8} + {\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} d^{9}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{9} - 4 \, {\left(a^{9} b^{3} + 3 \, a^{7} b^{5} + 3 \, a^{5} b^{7} + a^{3} b^{9}\right)} c^{8} d + 2 \, {\left(3 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 12 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{7} d^{2} - 4 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 9 \, a^{7} b^{5} + 7 \, a^{5} b^{7} + 2 \, a^{3} b^{9}\right)} c^{6} d^{3} + {\left(a^{12} + 15 \, a^{10} b^{2} + 40 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{5} d^{4} - 4 \, {\left(2 \, a^{11} b + 7 \, a^{9} b^{3} + 9 \, a^{7} b^{5} + 5 \, a^{5} b^{7} + a^{3} b^{9}\right)} c^{4} d^{5} + 2 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 12 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 3 \, a^{4} b^{8}\right)} c^{3} d^{6} - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} c^{2} d^{7} + {\left(a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6}\right)} c d^{8}\right)} f\right)}}"," ",0,"-1/2*((7*a^2*b^7 + b^9)*c^7 - 6*(3*a^3*b^6 + a*b^8)*c^6*d + (11*a^4*b^5 + 19*a^2*b^7 + 2*b^9)*c^5*d^2 - 12*(3*a^3*b^6 + a*b^8)*c^4*d^3 + (22*a^4*b^5 + 17*a^2*b^7 + b^9)*c^3*d^4 - 6*(3*a^3*b^6 + a*b^8)*c^2*d^5 - (2*a^8*b + 6*a^6*b^3 - 5*a^4*b^5 - 3*a^2*b^7)*c*d^6 + 2*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^7 - ((5*a^2*b^7 - b^9)*c^6*d - 2*(7*a^3*b^6 + a*b^8)*c^5*d^2 + (9*a^4*b^5 + 13*a^2*b^7 - 2*b^9)*c^4*d^3 - 4*(7*a^3*b^6 + a*b^8)*c^3*d^4 - (2*a^6*b^3 - 12*a^4*b^5 - 5*a^2*b^7 + 3*b^9)*c^2*d^5 + 2*(a^7*b^2 + 3*a^5*b^4 - 4*a^3*b^6)*c*d^6 + 3*(3*a^4*b^5 + a^2*b^7)*d^7 + 2*((a^3*b^6 - 3*a*b^8)*c^6*d - 2*(2*a^4*b^5 - 3*a^2*b^7 - b^9)*c^5*d^2 + (6*a^5*b^4 + 5*a^3*b^6 - 5*a*b^8)*c^4*d^3 - 4*(a^6*b^3 + 5*a^4*b^5)*c^3*d^4 + (a^7*b^2 + 15*a^5*b^4 + 10*a^3*b^6)*c^2*d^5 - 2*(a^6*b^3 + 5*a^4*b^5)*c*d^6 - (a^7*b^2 - 3*a^5*b^4)*d^7)*f*x)*tan(f*x + e)^3 - 2*((a^5*b^4 - 3*a^3*b^6)*c^7 - 2*(2*a^6*b^3 - 3*a^4*b^5 - a^2*b^7)*c^6*d + (6*a^7*b^2 + 5*a^5*b^4 - 5*a^3*b^6)*c^5*d^2 - 4*(a^8*b + 5*a^6*b^3)*c^4*d^3 + (a^9 + 15*a^7*b^2 + 10*a^5*b^4)*c^3*d^4 - 2*(a^8*b + 5*a^6*b^3)*c^2*d^5 - (a^9 - 3*a^7*b^2)*c*d^6)*f*x - ((5*a^2*b^7 - b^9)*c^7 - 8*(a^3*b^6 + a*b^8)*c^6*d - (7*a^4*b^5 - 25*a^2*b^7 - 2*b^9)*c^5*d^2 + 2*(5*a^5*b^4 - 11*a^3*b^6 - 10*a*b^8)*c^4*d^3 - 7*(2*a^4*b^5 - 5*a^2*b^7 - b^9)*c^3*d^4 - 4*(a^7*b^2 - 2*a^5*b^4 + 8*a^3*b^6 + 5*a*b^8)*c^2*d^5 + (4*a^8*b + 14*a^6*b^3 + 11*a^4*b^5 + 25*a^2*b^7 + 6*b^9)*c*d^6 - 2*(a^7*b^2 - 2*a^5*b^4 + 6*a^3*b^6 + 3*a*b^8)*d^7 + 2*((a^3*b^6 - 3*a*b^8)*c^7 - 2*(a^4*b^5 - b^9)*c^6*d - (2*a^5*b^4 - 17*a^3*b^6 + a*b^8)*c^5*d^2 + 2*(4*a^6*b^3 - 5*a^4*b^5 - 5*a^2*b^7)*c^4*d^3 - (7*a^7*b^2 + 25*a^5*b^4 - 10*a^3*b^6)*c^3*d^4 + 2*(a^8*b + 14*a^6*b^3 + 5*a^4*b^5)*c^2*d^5 - (5*a^7*b^2 + 17*a^5*b^4)*c*d^6 - 2*(a^8*b - 3*a^6*b^3)*d^7)*f*x)*tan(f*x + e)^2 - ((3*a^4*b^5 - a^2*b^7)*c^7 - 2*(5*a^5*b^4 + a^3*b^6)*c^6*d + (10*a^6*b^3 + 15*a^4*b^5 + a^2*b^7)*c^5*d^2 - 4*(5*a^5*b^4 + a^3*b^6)*c^4*d^3 + (20*a^6*b^3 + 21*a^4*b^5 + 5*a^2*b^7)*c^3*d^4 - 2*(5*a^5*b^4 + a^3*b^6)*c^2*d^5 + (10*a^6*b^3 + 9*a^4*b^5 + 3*a^2*b^7)*c*d^6 + ((3*a^2*b^7 - b^9)*c^6*d - 2*(5*a^3*b^6 + a*b^8)*c^5*d^2 + (10*a^4*b^5 + 15*a^2*b^7 + b^9)*c^4*d^3 - 4*(5*a^3*b^6 + a*b^8)*c^3*d^4 + (20*a^4*b^5 + 21*a^2*b^7 + 5*b^9)*c^2*d^5 - 2*(5*a^3*b^6 + a*b^8)*c*d^6 + (10*a^4*b^5 + 9*a^2*b^7 + 3*b^9)*d^7)*tan(f*x + e)^3 + ((3*a^2*b^7 - b^9)*c^7 - 4*(a^3*b^6 + a*b^8)*c^6*d - (10*a^4*b^5 - 11*a^2*b^7 - b^9)*c^5*d^2 + 2*(10*a^5*b^4 + 5*a^3*b^6 - a*b^8)*c^4*d^3 - (20*a^4*b^5 - 13*a^2*b^7 - 5*b^9)*c^3*d^4 + 8*(5*a^5*b^4 + 4*a^3*b^6 + a*b^8)*c^2*d^5 - (10*a^4*b^5 - 5*a^2*b^7 - 3*b^9)*c*d^6 + 2*(10*a^5*b^4 + 9*a^3*b^6 + 3*a*b^8)*d^7)*tan(f*x + e)^2 + (2*(3*a^3*b^6 - a*b^8)*c^7 - (17*a^4*b^5 + 5*a^2*b^7)*c^6*d + 2*(5*a^5*b^4 + 14*a^3*b^6 + a*b^8)*c^5*d^2 + (10*a^6*b^3 - 25*a^4*b^5 - 7*a^2*b^7)*c^4*d^3 + 2*(10*a^5*b^4 + 19*a^3*b^6 + 5*a*b^8)*c^3*d^4 + (20*a^6*b^3 + a^4*b^5 + a^2*b^7)*c^2*d^5 + 2*(5*a^5*b^4 + 8*a^3*b^6 + 3*a*b^8)*c*d^6 + (10*a^6*b^3 + 9*a^4*b^5 + 3*a^2*b^7)*d^7)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) + (5*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c^3*d^4 - 2*(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*c^2*d^5 + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c*d^6 + (5*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*c^2*d^5 - 2*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c*d^6 + 3*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*d^7)*tan(f*x + e)^3 + (5*(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*c^3*d^4 + 8*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^2*d^5 - (4*a^8*b + 9*a^6*b^3 + 3*a^4*b^5 - 5*a^2*b^7 - 3*b^9)*c*d^6 + 6*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*d^7)*tan(f*x + e)^2 + (10*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^3*d^4 + (a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c^2*d^5 - 2*(a^9 - 6*a^5*b^4 - 8*a^3*b^6 - 3*a*b^8)*c*d^6 + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (6*(a^3*b^6 - a*b^8)*c^7 - (16*a^4*b^5 - 5*a^2*b^7 - 3*b^9)*c^6*d + 2*(5*a^5*b^4 + 12*a^3*b^6 - 5*a*b^8)*c^5*d^2 - (43*a^4*b^5 - 5*a^2*b^7 - 6*b^9)*c^4*d^3 + 2*(10*a^5*b^4 + 15*a^3*b^6 - a*b^8)*c^3*d^4 - (2*a^8*b + 6*a^6*b^3 + 44*a^4*b^5 + 7*a^2*b^7 - 3*b^9)*c^2*d^5 + 2*(a^9 + 5*a^7*b^2 + 14*a^5*b^4 + 13*a^3*b^6 + 3*a*b^8)*c*d^6 - (4*a^8*b + 12*a^6*b^3 + 23*a^4*b^5 + 9*a^2*b^7)*d^7 + 2*(2*(a^4*b^5 - 3*a^2*b^7)*c^7 - (7*a^5*b^4 - 9*a^3*b^6 - 4*a*b^8)*c^6*d + 8*(a^6*b^3 + 2*a^4*b^5 - a^2*b^7)*c^5*d^2 - (2*a^7*b^2 + 35*a^5*b^4 + 5*a^3*b^6)*c^4*d^3 - 2*(a^8*b - 5*a^6*b^3 - 10*a^4*b^5)*c^3*d^4 + (a^9 + 11*a^7*b^2 - 10*a^5*b^4)*c^2*d^5 - 4*(a^8*b + a^6*b^3)*c*d^6 - (a^9 - 3*a^7*b^2)*d^7)*f*x)*tan(f*x + e))/(((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*c^8*d - 4*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*c^7*d^2 + 2*(3*a^8*b^4 + 10*a^6*b^6 + 12*a^4*b^8 + 6*a^2*b^10 + b^12)*c^6*d^3 - 4*(a^9*b^3 + 5*a^7*b^5 + 9*a^5*b^7 + 7*a^3*b^9 + 2*a*b^11)*c^5*d^4 + (a^10*b^2 + 15*a^8*b^4 + 40*a^6*b^6 + 40*a^4*b^8 + 15*a^2*b^10 + b^12)*c^4*d^5 - 4*(2*a^9*b^3 + 7*a^7*b^5 + 9*a^5*b^7 + 5*a^3*b^9 + a*b^11)*c^3*d^6 + 2*(a^10*b^2 + 6*a^8*b^4 + 12*a^6*b^6 + 10*a^4*b^8 + 3*a^2*b^10)*c^2*d^7 - 4*(a^9*b^3 + 3*a^7*b^5 + 3*a^5*b^7 + a^3*b^9)*c*d^8 + (a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*d^9)*f*tan(f*x + e)^3 + ((a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*c^9 - 2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*c^8*d - 2*(a^8*b^4 + 2*a^6*b^6 - 2*a^2*b^10 - b^12)*c^7*d^2 + 4*(2*a^9*b^3 + 5*a^7*b^5 + 3*a^5*b^7 - a^3*b^9 - a*b^11)*c^6*d^3 - (7*a^10*b^2 + 25*a^8*b^4 + 32*a^6*b^6 + 16*a^4*b^8 + a^2*b^10 - b^12)*c^5*d^4 + 2*(a^11*b + 11*a^9*b^3 + 26*a^7*b^5 + 22*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c^4*d^5 - 2*(7*a^10*b^2 + 22*a^8*b^4 + 24*a^6*b^6 + 10*a^4*b^8 + a^2*b^10)*c^3*d^6 + 4*(a^11*b + 5*a^9*b^3 + 9*a^7*b^5 + 7*a^5*b^7 + 2*a^3*b^9)*c^2*d^7 - 7*(a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*c*d^8 + 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*d^9)*f*tan(f*x + e)^2 + (2*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*c^9 - 7*(a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*c^8*d + 4*(2*a^9*b^3 + 7*a^7*b^5 + 9*a^5*b^7 + 5*a^3*b^9 + a*b^11)*c^7*d^2 - 2*(a^10*b^2 + 10*a^8*b^4 + 24*a^6*b^6 + 22*a^4*b^8 + 7*a^2*b^10)*c^6*d^3 - 2*(a^11*b - 5*a^9*b^3 - 22*a^7*b^5 - 26*a^5*b^7 - 11*a^3*b^9 - a*b^11)*c^5*d^4 + (a^12 - a^10*b^2 - 16*a^8*b^4 - 32*a^6*b^6 - 25*a^4*b^8 - 7*a^2*b^10)*c^4*d^5 - 4*(a^11*b + a^9*b^3 - 3*a^7*b^5 - 5*a^5*b^7 - 2*a^3*b^9)*c^3*d^6 + 2*(a^12 + 2*a^10*b^2 - 2*a^6*b^6 - a^4*b^8)*c^2*d^7 - 2*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*c*d^8 + (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*d^9)*f*tan(f*x + e) + ((a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*c^9 - 4*(a^9*b^3 + 3*a^7*b^5 + 3*a^5*b^7 + a^3*b^9)*c^8*d + 2*(3*a^10*b^2 + 10*a^8*b^4 + 12*a^6*b^6 + 6*a^4*b^8 + a^2*b^10)*c^7*d^2 - 4*(a^11*b + 5*a^9*b^3 + 9*a^7*b^5 + 7*a^5*b^7 + 2*a^3*b^9)*c^6*d^3 + (a^12 + 15*a^10*b^2 + 40*a^8*b^4 + 40*a^6*b^6 + 15*a^4*b^8 + a^2*b^10)*c^5*d^4 - 4*(2*a^11*b + 7*a^9*b^3 + 9*a^7*b^5 + 5*a^5*b^7 + a^3*b^9)*c^4*d^5 + 2*(a^12 + 6*a^10*b^2 + 12*a^8*b^4 + 10*a^6*b^6 + 3*a^4*b^8)*c^3*d^6 - 4*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*c^2*d^7 + (a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6)*c*d^8)*f)","B",0
1223,1,1247,0,0.936714," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{b^{4} c^{6} d^{2} + 4 \, a b^{3} c^{5} d^{3} - 4 \, a^{3} b c d^{7} - a^{4} d^{8} - {\left(18 \, a^{2} b^{2} - 7 \, b^{4}\right)} c^{4} d^{4} + 20 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{5} - {\left(7 \, a^{4} - 18 \, a^{2} b^{2}\right)} c^{2} d^{6} + 2 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{5} d^{3} + 12 \, {\left(a^{3} b - a b^{3}\right)} c^{4} d^{4} - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{5} - 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{6}\right)} f x - {\left(3 \, b^{4} c^{6} d^{2} - 4 \, a b^{3} c^{5} d^{3} - 12 \, a^{3} b c d^{7} + a^{4} d^{8} - 3 \, {\left(2 \, a^{2} b^{2} - 3 \, b^{4}\right)} c^{4} d^{4} + 4 \, {\left(3 \, a^{3} b - 7 \, a b^{3}\right)} c^{3} d^{5} - 5 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c^{2} d^{6} - 2 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{5} + 12 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{6} - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{7} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{8}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(b^{4} c^{8} + 3 \, b^{4} c^{6} d^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c^{5} d^{3} + 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{4} d^{4} + 12 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{5} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c^{2} d^{6} + {\left(b^{4} c^{6} d^{2} + 3 \, b^{4} c^{4} d^{4} - 4 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{5} + 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{2} d^{6} + 12 \, {\left(a^{3} b - a b^{3}\right)} c d^{7} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b^{4} c^{7} d + 3 \, b^{4} c^{5} d^{3} - 4 \, {\left(a^{3} b - a b^{3}\right)} c^{4} d^{4} + 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{3} d^{5} + 12 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{6} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(b^{4} c^{8} + 3 \, b^{4} c^{6} d^{2} + 3 \, b^{4} c^{4} d^{4} + b^{4} c^{2} d^{6} + {\left(b^{4} c^{6} d^{2} + 3 \, b^{4} c^{4} d^{4} + 3 \, b^{4} c^{2} d^{6} + b^{4} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b^{4} c^{7} d + 3 \, b^{4} c^{5} d^{3} + 3 \, b^{4} c^{3} d^{5} + b^{4} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{1}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b^{4} c^{7} d + 4 \, a^{3} b d^{8} - 3 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} c^{5} d^{3} + 4 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c^{4} d^{4} - {\left(3 \, a^{4} - 18 \, a^{2} b^{2} + 4 \, b^{4}\right)} c^{3} d^{5} - 12 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d^{6} + 3 \, {\left(a^{4} - 4 \, a^{2} b^{2}\right)} c d^{7} - 2 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} + 12 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{5} - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{6} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{5} + 3 \, c^{4} d^{7} + 3 \, c^{2} d^{9} + d^{11}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d^{4} + 3 \, c^{5} d^{6} + 3 \, c^{3} d^{8} + c d^{10}\right)} f \tan\left(f x + e\right) + {\left(c^{8} d^{3} + 3 \, c^{6} d^{5} + 3 \, c^{4} d^{7} + c^{2} d^{9}\right)} f\right)}}"," ",0,"1/2*(b^4*c^6*d^2 + 4*a*b^3*c^5*d^3 - 4*a^3*b*c*d^7 - a^4*d^8 - (18*a^2*b^2 - 7*b^4)*c^4*d^4 + 20*(a^3*b - a*b^3)*c^3*d^5 - (7*a^4 - 18*a^2*b^2)*c^2*d^6 + 2*((a^4 - 6*a^2*b^2 + b^4)*c^5*d^3 + 12*(a^3*b - a*b^3)*c^4*d^4 - 3*(a^4 - 6*a^2*b^2 + b^4)*c^3*d^5 - 4*(a^3*b - a*b^3)*c^2*d^6)*f*x - (3*b^4*c^6*d^2 - 4*a*b^3*c^5*d^3 - 12*a^3*b*c*d^7 + a^4*d^8 - 3*(2*a^2*b^2 - 3*b^4)*c^4*d^4 + 4*(3*a^3*b - 7*a*b^3)*c^3*d^5 - 5*(a^4 - 6*a^2*b^2)*c^2*d^6 - 2*((a^4 - 6*a^2*b^2 + b^4)*c^3*d^5 + 12*(a^3*b - a*b^3)*c^2*d^6 - 3*(a^4 - 6*a^2*b^2 + b^4)*c*d^7 - 4*(a^3*b - a*b^3)*d^8)*f*x)*tan(f*x + e)^2 + (b^4*c^8 + 3*b^4*c^6*d^2 - 4*(a^3*b - a*b^3)*c^5*d^3 + 3*(a^4 - 6*a^2*b^2 + 2*b^4)*c^4*d^4 + 12*(a^3*b - a*b^3)*c^3*d^5 - (a^4 - 6*a^2*b^2)*c^2*d^6 + (b^4*c^6*d^2 + 3*b^4*c^4*d^4 - 4*(a^3*b - a*b^3)*c^3*d^5 + 3*(a^4 - 6*a^2*b^2 + 2*b^4)*c^2*d^6 + 12*(a^3*b - a*b^3)*c*d^7 - (a^4 - 6*a^2*b^2)*d^8)*tan(f*x + e)^2 + 2*(b^4*c^7*d + 3*b^4*c^5*d^3 - 4*(a^3*b - a*b^3)*c^4*d^4 + 3*(a^4 - 6*a^2*b^2 + 2*b^4)*c^3*d^5 + 12*(a^3*b - a*b^3)*c^2*d^6 - (a^4 - 6*a^2*b^2)*c*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (b^4*c^8 + 3*b^4*c^6*d^2 + 3*b^4*c^4*d^4 + b^4*c^2*d^6 + (b^4*c^6*d^2 + 3*b^4*c^4*d^4 + 3*b^4*c^2*d^6 + b^4*d^8)*tan(f*x + e)^2 + 2*(b^4*c^7*d + 3*b^4*c^5*d^3 + 3*b^4*c^3*d^5 + b^4*c*d^7)*tan(f*x + e))*log(1/(tan(f*x + e)^2 + 1)) - 2*(b^4*c^7*d + 4*a^3*b*d^8 - 3*(2*a^2*b^2 - b^4)*c^5*d^3 + 4*(2*a^3*b - 3*a*b^3)*c^4*d^4 - (3*a^4 - 18*a^2*b^2 + 4*b^4)*c^3*d^5 - 12*(a^3*b - a*b^3)*c^2*d^6 + 3*(a^4 - 4*a^2*b^2)*c*d^7 - 2*((a^4 - 6*a^2*b^2 + b^4)*c^4*d^4 + 12*(a^3*b - a*b^3)*c^3*d^5 - 3*(a^4 - 6*a^2*b^2 + b^4)*c^2*d^6 - 4*(a^3*b - a*b^3)*c*d^7)*f*x)*tan(f*x + e))/((c^6*d^5 + 3*c^4*d^7 + 3*c^2*d^9 + d^11)*f*tan(f*x + e)^2 + 2*(c^7*d^4 + 3*c^5*d^6 + 3*c^3*d^8 + c*d^10)*f*tan(f*x + e) + (c^8*d^3 + 3*c^6*d^5 + 3*c^4*d^7 + c^2*d^9)*f)","B",0
1224,1,861,0,0.792652," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{b^{3} c^{5} - 9 \, a b^{2} c^{4} d - 3 \, a^{2} b c d^{4} - a^{3} d^{5} + 5 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{3} d^{2} - {\left(7 \, a^{3} - 9 \, a b^{2}\right)} c^{2} d^{3} + 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{5} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{4} d - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d^{3}\right)} f x + {\left(b^{3} c^{5} + 3 \, a b^{2} c^{4} d + 9 \, a^{2} b c d^{4} - a^{3} d^{5} - {\left(9 \, a^{2} b - 7 \, b^{3}\right)} c^{3} d^{2} + 5 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d^{3} + 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{3} d^{2} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d^{3} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{4} - {\left(3 \, a^{2} b - b^{3}\right)} d^{5}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{5} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{4} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{3} d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d^{3} + {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} d^{2} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d^{3} - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{4} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{4} d - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} d^{2} - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d^{3} + {\left(a^{3} - 3 \, a b^{2}\right)} c d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) + 2 \, {\left(3 \, a b^{2} c^{5} - 3 \, a^{2} b d^{5} - 3 \, {\left(2 \, a^{2} b - b^{3}\right)} c^{4} d + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{3} d^{2} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d^{3} - 3 \, {\left(a^{3} - 2 \, a b^{2}\right)} c d^{4} + 2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{4} d + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{3} d^{2} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d^{3} - {\left(3 \, a^{2} b - b^{3}\right)} c d^{4}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d + 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} + c d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{8} + 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} + c^{2} d^{6}\right)} f\right)}}"," ",0,"1/2*(b^3*c^5 - 9*a*b^2*c^4*d - 3*a^2*b*c*d^4 - a^3*d^5 + 5*(3*a^2*b - b^3)*c^3*d^2 - (7*a^3 - 9*a*b^2)*c^2*d^3 + 2*((a^3 - 3*a*b^2)*c^5 + 3*(3*a^2*b - b^3)*c^4*d - 3*(a^3 - 3*a*b^2)*c^3*d^2 - (3*a^2*b - b^3)*c^2*d^3)*f*x + (b^3*c^5 + 3*a*b^2*c^4*d + 9*a^2*b*c*d^4 - a^3*d^5 - (9*a^2*b - 7*b^3)*c^3*d^2 + 5*(a^3 - 3*a*b^2)*c^2*d^3 + 2*((a^3 - 3*a*b^2)*c^3*d^2 + 3*(3*a^2*b - b^3)*c^2*d^3 - 3*(a^3 - 3*a*b^2)*c*d^4 - (3*a^2*b - b^3)*d^5)*f*x)*tan(f*x + e)^2 - ((3*a^2*b - b^3)*c^5 - 3*(a^3 - 3*a*b^2)*c^4*d - 3*(3*a^2*b - b^3)*c^3*d^2 + (a^3 - 3*a*b^2)*c^2*d^3 + ((3*a^2*b - b^3)*c^3*d^2 - 3*(a^3 - 3*a*b^2)*c^2*d^3 - 3*(3*a^2*b - b^3)*c*d^4 + (a^3 - 3*a*b^2)*d^5)*tan(f*x + e)^2 + 2*((3*a^2*b - b^3)*c^4*d - 3*(a^3 - 3*a*b^2)*c^3*d^2 - 3*(3*a^2*b - b^3)*c^2*d^3 + (a^3 - 3*a*b^2)*c*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) + 2*(3*a*b^2*c^5 - 3*a^2*b*d^5 - 3*(2*a^2*b - b^3)*c^4*d + 3*(a^3 - 3*a*b^2)*c^3*d^2 + 3*(3*a^2*b - b^3)*c^2*d^3 - 3*(a^3 - 2*a*b^2)*c*d^4 + 2*((a^3 - 3*a*b^2)*c^4*d + 3*(3*a^2*b - b^3)*c^3*d^2 - 3*(a^3 - 3*a*b^2)*c^2*d^3 - (3*a^2*b - b^3)*c*d^4)*f*x)*tan(f*x + e))/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*f*tan(f*x + e)^2 + 2*(c^7*d + 3*c^5*d^3 + 3*c^3*d^5 + c*d^7)*f*tan(f*x + e) + (c^8 + 3*c^6*d^2 + 3*c^4*d^4 + c^2*d^6)*f)","B",0
1225,1,663,0,0.493392," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{3 \, b^{2} c^{4} d - 10 \, a b c^{3} d^{2} + 2 \, a b c d^{4} + a^{2} d^{5} + {\left(7 \, a^{2} - 3 \, b^{2}\right)} c^{2} d^{3} - 2 \, {\left(6 \, a b c^{4} d - 2 \, a b c^{2} d^{3} + {\left(a^{2} - b^{2}\right)} c^{5} - 3 \, {\left(a^{2} - b^{2}\right)} c^{3} d^{2}\right)} f x - {\left(b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + 6 \, a b c d^{4} - a^{2} d^{5} + 5 \, {\left(a^{2} - b^{2}\right)} c^{2} d^{3} + 2 \, {\left(6 \, a b c^{2} d^{3} - 2 \, a b d^{5} + {\left(a^{2} - b^{2}\right)} c^{3} d^{2} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{4}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, a b c^{5} - 6 \, a b c^{3} d^{2} - 3 \, {\left(a^{2} - b^{2}\right)} c^{4} d + {\left(a^{2} - b^{2}\right)} c^{2} d^{3} + {\left(2 \, a b c^{3} d^{2} - 6 \, a b c d^{4} - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d^{3} + {\left(a^{2} - b^{2}\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(2 \, a b c^{4} d - 6 \, a b c^{2} d^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c^{3} d^{2} + {\left(a^{2} - b^{2}\right)} c d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(b^{2} c^{5} - 4 \, a b c^{4} d + 6 \, a b c^{2} d^{3} - 2 \, a b d^{5} + 3 \, {\left(a^{2} - b^{2}\right)} c^{3} d^{2} - {\left(3 \, a^{2} - 2 \, b^{2}\right)} c d^{4} + 2 \, {\left(6 \, a b c^{3} d^{2} - 2 \, a b c d^{4} + {\left(a^{2} - b^{2}\right)} c^{4} d - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d^{3}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d + 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} + c d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{8} + 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} + c^{2} d^{6}\right)} f\right)}}"," ",0,"-1/2*(3*b^2*c^4*d - 10*a*b*c^3*d^2 + 2*a*b*c*d^4 + a^2*d^5 + (7*a^2 - 3*b^2)*c^2*d^3 - 2*(6*a*b*c^4*d - 2*a*b*c^2*d^3 + (a^2 - b^2)*c^5 - 3*(a^2 - b^2)*c^3*d^2)*f*x - (b^2*c^4*d - 6*a*b*c^3*d^2 + 6*a*b*c*d^4 - a^2*d^5 + 5*(a^2 - b^2)*c^2*d^3 + 2*(6*a*b*c^2*d^3 - 2*a*b*d^5 + (a^2 - b^2)*c^3*d^2 - 3*(a^2 - b^2)*c*d^4)*f*x)*tan(f*x + e)^2 + (2*a*b*c^5 - 6*a*b*c^3*d^2 - 3*(a^2 - b^2)*c^4*d + (a^2 - b^2)*c^2*d^3 + (2*a*b*c^3*d^2 - 6*a*b*c*d^4 - 3*(a^2 - b^2)*c^2*d^3 + (a^2 - b^2)*d^5)*tan(f*x + e)^2 + 2*(2*a*b*c^4*d - 6*a*b*c^2*d^3 - 3*(a^2 - b^2)*c^3*d^2 + (a^2 - b^2)*c*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(b^2*c^5 - 4*a*b*c^4*d + 6*a*b*c^2*d^3 - 2*a*b*d^5 + 3*(a^2 - b^2)*c^3*d^2 - (3*a^2 - 2*b^2)*c*d^4 + 2*(6*a*b*c^3*d^2 - 2*a*b*c*d^4 + (a^2 - b^2)*c^4*d - 3*(a^2 - b^2)*c^2*d^3)*f*x)*tan(f*x + e))/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*f*tan(f*x + e)^2 + 2*(c^7*d + 3*c^5*d^3 + 3*c^3*d^5 + c*d^7)*f*tan(f*x + e) + (c^8 + 3*c^6*d^2 + 3*c^4*d^4 + c^2*d^6)*f)","B",0
1226,1,482,0,0.498930," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{5 \, b c^{3} d^{2} - 7 \, a c^{2} d^{3} - b c d^{4} - a d^{5} + 2 \, {\left(a c^{5} + 3 \, b c^{4} d - 3 \, a c^{3} d^{2} - b c^{2} d^{3}\right)} f x - {\left(3 \, b c^{3} d^{2} - 5 \, a c^{2} d^{3} - 3 \, b c d^{4} + a d^{5} - 2 \, {\left(a c^{3} d^{2} + 3 \, b c^{2} d^{3} - 3 \, a c d^{4} - b d^{5}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left(b c^{5} - 3 \, a c^{4} d - 3 \, b c^{3} d^{2} + a c^{2} d^{3} + {\left(b c^{3} d^{2} - 3 \, a c^{2} d^{3} - 3 \, b c d^{4} + a d^{5}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b c^{4} d - 3 \, a c^{3} d^{2} - 3 \, b c^{2} d^{3} + a c d^{4}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(2 \, b c^{4} d - 3 \, a c^{3} d^{2} - 3 \, b c^{2} d^{3} + 3 \, a c d^{4} + b d^{5} - 2 \, {\left(a c^{4} d + 3 \, b c^{3} d^{2} - 3 \, a c^{2} d^{3} - b c d^{4}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{7} d + 3 \, c^{5} d^{3} + 3 \, c^{3} d^{5} + c d^{7}\right)} f \tan\left(f x + e\right) + {\left(c^{8} + 3 \, c^{6} d^{2} + 3 \, c^{4} d^{4} + c^{2} d^{6}\right)} f\right)}}"," ",0,"1/2*(5*b*c^3*d^2 - 7*a*c^2*d^3 - b*c*d^4 - a*d^5 + 2*(a*c^5 + 3*b*c^4*d - 3*a*c^3*d^2 - b*c^2*d^3)*f*x - (3*b*c^3*d^2 - 5*a*c^2*d^3 - 3*b*c*d^4 + a*d^5 - 2*(a*c^3*d^2 + 3*b*c^2*d^3 - 3*a*c*d^4 - b*d^5)*f*x)*tan(f*x + e)^2 - (b*c^5 - 3*a*c^4*d - 3*b*c^3*d^2 + a*c^2*d^3 + (b*c^3*d^2 - 3*a*c^2*d^3 - 3*b*c*d^4 + a*d^5)*tan(f*x + e)^2 + 2*(b*c^4*d - 3*a*c^3*d^2 - 3*b*c^2*d^3 + a*c*d^4)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(2*b*c^4*d - 3*a*c^3*d^2 - 3*b*c^2*d^3 + 3*a*c*d^4 + b*d^5 - 2*(a*c^4*d + 3*b*c^3*d^2 - 3*a*c^2*d^3 - b*c*d^4)*f*x)*tan(f*x + e))/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*f*tan(f*x + e)^2 + 2*(c^7*d + 3*c^5*d^3 + 3*c^3*d^5 + c*d^7)*f*tan(f*x + e) + (c^8 + 3*c^6*d^2 + 3*c^4*d^4 + c^2*d^6)*f)","B",0
1227,1,1841,0,2.471226," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","\frac{9 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} - 16 \, {\left(a^{3} b + a b^{3}\right)} c^{3} d^{5} + {\left(7 \, a^{4} + 10 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} d^{6} - 4 \, {\left(a^{3} b + a b^{3}\right)} c d^{7} + {\left(a^{4} + a^{2} b^{2}\right)} d^{8} + 2 \, {\left(a b^{3} c^{8} - a^{3} b c^{2} d^{6} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{7} d + 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} c^{6} d^{2} - {\left(a^{4} - b^{4}\right)} c^{5} d^{3} - 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} c^{4} d^{4} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} d^{5}\right)} f x - {\left(7 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{3} d^{5} + {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{6} - {\left(a^{4} + a^{2} b^{2}\right)} d^{8} - 2 \, {\left(a b^{3} c^{6} d^{2} - a^{3} b d^{8} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{5} d^{3} + 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} c^{4} d^{4} - {\left(a^{4} - b^{4}\right)} c^{3} d^{5} - 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} c^{2} d^{6} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{7}\right)} f x\right)} \tan\left(f x + e\right)^{2} + {\left(b^{4} c^{8} + 3 \, b^{4} c^{6} d^{2} + 3 \, b^{4} c^{4} d^{4} + b^{4} c^{2} d^{6} + {\left(b^{4} c^{6} d^{2} + 3 \, b^{4} c^{4} d^{4} + 3 \, b^{4} c^{2} d^{6} + b^{4} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b^{4} c^{7} d + 3 \, b^{4} c^{5} d^{3} + 3 \, b^{4} c^{3} d^{5} + b^{4} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{6} d^{2} - 8 \, {\left(a^{3} b + a b^{3}\right)} c^{5} d^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} - {\left(a^{4} - b^{4}\right)} c^{2} d^{6} + {\left(6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} - 8 \, {\left(a^{3} b + a b^{3}\right)} c^{3} d^{5} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{6} - {\left(a^{4} - b^{4}\right)} d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{5} d^{3} - 8 \, {\left(a^{3} b + a b^{3}\right)} c^{4} d^{4} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} d^{5} - {\left(a^{4} - b^{4}\right)} c d^{7}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - 2 \, {\left(4 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{5} d^{3} - 7 \, {\left(a^{3} b + a b^{3}\right)} c^{4} d^{4} + 3 \, {\left(a^{4} - b^{4}\right)} c^{3} d^{5} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d^{6} - {\left(3 \, a^{4} + 4 \, a^{2} b^{2} + b^{4}\right)} c d^{7} + {\left(a^{3} b + a b^{3}\right)} d^{8} - 2 \, {\left(a b^{3} c^{7} d - a^{3} b c d^{7} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{6} d^{2} + 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} c^{5} d^{3} - {\left(a^{4} - b^{4}\right)} c^{4} d^{4} - 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} c^{3} d^{5} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d^{6}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{2} b^{3} + b^{5}\right)} c^{9} d^{2} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{8} d^{3} + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{7} d^{4} - {\left(a^{5} + 10 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{6} d^{5} + 3 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5}\right)} c^{5} d^{6} - 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{4} d^{7} + {\left(9 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} c^{3} d^{8} - 3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} d^{9} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c d^{10} - {\left(a^{5} + a^{3} b^{2}\right)} d^{11}\right)} f \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{10} d - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{9} d^{2} + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{8} d^{3} - {\left(a^{5} + 10 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{7} d^{4} + 3 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5}\right)} c^{6} d^{5} - 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{5} d^{6} + {\left(9 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} c^{4} d^{7} - 3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} d^{8} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{2} d^{9} - {\left(a^{5} + a^{3} b^{2}\right)} c d^{10}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{11} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{10} d + 3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{9} d^{2} - {\left(a^{5} + 10 \, a^{3} b^{2} + 9 \, a b^{4}\right)} c^{8} d^{3} + 3 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5}\right)} c^{7} d^{4} - 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{6} d^{5} + {\left(9 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} c^{5} d^{6} - 3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{4} d^{7} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{3} d^{8} - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d^{9}\right)} f\right)}}"," ",0,"1/2*(9*(a^2*b^2 + b^4)*c^4*d^4 - 16*(a^3*b + a*b^3)*c^3*d^5 + (7*a^4 + 10*a^2*b^2 + 3*b^4)*c^2*d^6 - 4*(a^3*b + a*b^3)*c*d^7 + (a^4 + a^2*b^2)*d^8 + 2*(a*b^3*c^8 - a^3*b*c^2*d^6 - 3*(a^2*b^2 + b^4)*c^7*d + 3*(a^3*b + 2*a*b^3)*c^6*d^2 - (a^4 - b^4)*c^5*d^3 - 3*(2*a^3*b + a*b^3)*c^4*d^4 + 3*(a^4 + a^2*b^2)*c^3*d^5)*f*x - (7*(a^2*b^2 + b^4)*c^4*d^4 - 12*(a^3*b + a*b^3)*c^3*d^5 + (5*a^4 + 6*a^2*b^2 + b^4)*c^2*d^6 - (a^4 + a^2*b^2)*d^8 - 2*(a*b^3*c^6*d^2 - a^3*b*d^8 - 3*(a^2*b^2 + b^4)*c^5*d^3 + 3*(a^3*b + 2*a*b^3)*c^4*d^4 - (a^4 - b^4)*c^3*d^5 - 3*(2*a^3*b + a*b^3)*c^2*d^6 + 3*(a^4 + a^2*b^2)*c*d^7)*f*x)*tan(f*x + e)^2 + (b^4*c^8 + 3*b^4*c^6*d^2 + 3*b^4*c^4*d^4 + b^4*c^2*d^6 + (b^4*c^6*d^2 + 3*b^4*c^4*d^4 + 3*b^4*c^2*d^6 + b^4*d^8)*tan(f*x + e)^2 + 2*(b^4*c^7*d + 3*b^4*c^5*d^3 + 3*b^4*c^3*d^5 + b^4*c*d^7)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (6*(a^2*b^2 + b^4)*c^6*d^2 - 8*(a^3*b + a*b^3)*c^5*d^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^4 - (a^4 - b^4)*c^2*d^6 + (6*(a^2*b^2 + b^4)*c^4*d^4 - 8*(a^3*b + a*b^3)*c^3*d^5 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^6 - (a^4 - b^4)*d^8)*tan(f*x + e)^2 + 2*(6*(a^2*b^2 + b^4)*c^5*d^3 - 8*(a^3*b + a*b^3)*c^4*d^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^3*d^5 - (a^4 - b^4)*c*d^7)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - 2*(4*(a^2*b^2 + b^4)*c^5*d^3 - 7*(a^3*b + a*b^3)*c^4*d^4 + 3*(a^4 - b^4)*c^3*d^5 + 6*(a^3*b + a*b^3)*c^2*d^6 - (3*a^4 + 4*a^2*b^2 + b^4)*c*d^7 + (a^3*b + a*b^3)*d^8 - 2*(a*b^3*c^7*d - a^3*b*c*d^7 - 3*(a^2*b^2 + b^4)*c^6*d^2 + 3*(a^3*b + 2*a*b^3)*c^5*d^3 - (a^4 - b^4)*c^4*d^4 - 3*(2*a^3*b + a*b^3)*c^3*d^5 + 3*(a^4 + a^2*b^2)*c^2*d^6)*f*x)*tan(f*x + e))/(((a^2*b^3 + b^5)*c^9*d^2 - 3*(a^3*b^2 + a*b^4)*c^8*d^3 + 3*(a^4*b + 2*a^2*b^3 + b^5)*c^7*d^4 - (a^5 + 10*a^3*b^2 + 9*a*b^4)*c^6*d^5 + 3*(3*a^4*b + 4*a^2*b^3 + b^5)*c^5*d^6 - 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*c^4*d^7 + (9*a^4*b + 10*a^2*b^3 + b^5)*c^3*d^8 - 3*(a^5 + 2*a^3*b^2 + a*b^4)*c^2*d^9 + 3*(a^4*b + a^2*b^3)*c*d^10 - (a^5 + a^3*b^2)*d^11)*f*tan(f*x + e)^2 + 2*((a^2*b^3 + b^5)*c^10*d - 3*(a^3*b^2 + a*b^4)*c^9*d^2 + 3*(a^4*b + 2*a^2*b^3 + b^5)*c^8*d^3 - (a^5 + 10*a^3*b^2 + 9*a*b^4)*c^7*d^4 + 3*(3*a^4*b + 4*a^2*b^3 + b^5)*c^6*d^5 - 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*c^5*d^6 + (9*a^4*b + 10*a^2*b^3 + b^5)*c^4*d^7 - 3*(a^5 + 2*a^3*b^2 + a*b^4)*c^3*d^8 + 3*(a^4*b + a^2*b^3)*c^2*d^9 - (a^5 + a^3*b^2)*c*d^10)*f*tan(f*x + e) + ((a^2*b^3 + b^5)*c^11 - 3*(a^3*b^2 + a*b^4)*c^10*d + 3*(a^4*b + 2*a^2*b^3 + b^5)*c^9*d^2 - (a^5 + 10*a^3*b^2 + 9*a*b^4)*c^8*d^3 + 3*(3*a^4*b + 4*a^2*b^3 + b^5)*c^7*d^4 - 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*c^6*d^5 + (9*a^4*b + 10*a^2*b^3 + b^5)*c^5*d^6 - 3*(a^5 + 2*a^3*b^2 + a*b^4)*c^4*d^7 + 3*(a^4*b + a^2*b^3)*c^3*d^8 - (a^5 + a^3*b^2)*c^2*d^9)*f)","B",0
1228,1,4799,0,5.226626," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{7} c^{9} - 2 \, a b^{6} c^{8} d + 6 \, b^{7} c^{7} d^{2} - 6 \, a b^{6} c^{6} d^{3} + 6 \, b^{7} c^{5} d^{4} + {\left(11 \, a^{5} b^{2} + 22 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{4} d^{5} - 2 \, {\left(9 \, a^{6} b + 18 \, a^{4} b^{3} + 9 \, a^{2} b^{5} - b^{7}\right)} c^{3} d^{6} + {\left(7 \, a^{7} + 19 \, a^{5} b^{2} + 17 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c^{2} d^{7} - 6 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{8} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{9} - {\left(2 \, a b^{6} c^{7} d^{2} - 2 \, a^{2} b^{5} c^{6} d^{3} + 6 \, a b^{6} c^{5} d^{4} + 3 \, {\left(3 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{4} d^{5} - 2 \, {\left(7 \, a^{5} b^{2} + 14 \, a^{3} b^{4} + 4 \, a b^{6}\right)} c^{3} d^{6} + {\left(5 \, a^{6} b + 13 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{2} d^{7} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4}\right)} c d^{8} - {\left(a^{6} b + 2 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} d^{9} + 2 \, {\left(6 \, a^{5} b^{2} c^{2} d^{7} + 2 \, a^{5} b^{2} d^{9} + {\left(a^{2} b^{5} - b^{7}\right)} c^{7} d^{2} - 2 \, {\left(2 \, a^{3} b^{4} + a b^{6}\right)} c^{6} d^{3} + 3 \, {\left(2 \, a^{4} b^{3} + 5 \, a^{2} b^{5} + b^{7}\right)} c^{5} d^{4} - 2 \, {\left(2 \, a^{5} b^{2} + 10 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{4} d^{5} + {\left(a^{6} b + 5 \, a^{4} b^{3} + 10 \, a^{2} b^{5}\right)} c^{3} d^{6} - {\left(3 \, a^{6} b + 5 \, a^{4} b^{3}\right)} c d^{8}\right)} f x\right)} \tan\left(f x + e\right)^{3} - 2 \, {\left(6 \, a^{6} b c^{4} d^{5} + 2 \, a^{6} b c^{2} d^{7} + {\left(a^{3} b^{4} - a b^{6}\right)} c^{9} - 2 \, {\left(2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{8} d + 3 \, {\left(2 \, a^{5} b^{2} + 5 \, a^{3} b^{4} + a b^{6}\right)} c^{7} d^{2} - 2 \, {\left(2 \, a^{6} b + 10 \, a^{4} b^{3} + 5 \, a^{2} b^{5}\right)} c^{6} d^{3} + {\left(a^{7} + 5 \, a^{5} b^{2} + 10 \, a^{3} b^{4}\right)} c^{5} d^{4} - {\left(3 \, a^{7} + 5 \, a^{5} b^{2}\right)} c^{3} d^{6}\right)} f x - {\left(4 \, a b^{6} c^{8} d + 14 \, a b^{6} c^{6} d^{3} - 2 \, {\left(2 \, a^{2} b^{5} + b^{7}\right)} c^{7} d^{2} + 2 \, {\left(5 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 2 \, b^{7}\right)} c^{5} d^{4} - {\left(7 \, a^{5} b^{2} + 14 \, a^{3} b^{4} - 11 \, a b^{6}\right)} c^{4} d^{5} - 2 \, {\left(4 \, a^{6} b + 11 \, a^{4} b^{3} + 16 \, a^{2} b^{5} + 6 \, b^{7}\right)} c^{3} d^{6} + 5 \, {\left(a^{7} + 5 \, a^{5} b^{2} + 7 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{2} d^{7} - 2 \, {\left(4 \, a^{6} b + 10 \, a^{4} b^{3} + 10 \, a^{2} b^{5} + 3 \, b^{7}\right)} c d^{8} - {\left(a^{7} - 2 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - 6 \, a b^{6}\right)} d^{9} - 2 \, {\left(10 \, a^{4} b^{3} c^{2} d^{7} - 2 \, a^{6} b d^{9} - 2 \, {\left(a^{2} b^{5} - b^{7}\right)} c^{8} d + {\left(7 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{7} d^{2} - 2 \, {\left(4 \, a^{4} b^{3} + 14 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{6} d^{3} + {\left(2 \, a^{5} b^{2} + 25 \, a^{3} b^{4} + 17 \, a b^{6}\right)} c^{5} d^{4} + 2 \, {\left(a^{6} b + 5 \, a^{4} b^{3} - 5 \, a^{2} b^{5}\right)} c^{4} d^{5} - {\left(a^{7} + 17 \, a^{5} b^{2} + 10 \, a^{3} b^{4}\right)} c^{3} d^{6} + {\left(3 \, a^{7} + a^{5} b^{2}\right)} c d^{8}\right)} f x\right)} \tan\left(f x + e\right)^{2} - {\left(2 \, a^{2} b^{5} c^{9} + 6 \, a^{2} b^{5} c^{7} d^{2} + 6 \, a^{2} b^{5} c^{5} d^{4} + 2 \, a^{2} b^{5} c^{3} d^{6} - {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c^{8} d - 3 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c^{6} d^{3} - 3 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c^{4} d^{5} - {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c^{2} d^{7} + {\left(2 \, a b^{6} c^{7} d^{2} + 6 \, a b^{6} c^{5} d^{4} + 6 \, a b^{6} c^{3} d^{6} + 2 \, a b^{6} c d^{8} - {\left(5 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{6} d^{3} - 3 \, {\left(5 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{4} d^{5} - 3 \, {\left(5 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{2} d^{7} - {\left(5 \, a^{2} b^{5} + 3 \, b^{7}\right)} d^{9}\right)} \tan\left(f x + e\right)^{3} + {\left(4 \, a b^{6} c^{8} d - 2 \, {\left(4 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{7} d^{2} - {\left(5 \, a^{3} b^{4} - 9 \, a b^{6}\right)} c^{6} d^{3} - 6 \, {\left(4 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{5} d^{4} - 3 \, {\left(5 \, a^{3} b^{4} - a b^{6}\right)} c^{4} d^{5} - 6 \, {\left(4 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{3} d^{6} - 5 \, {\left(3 \, a^{3} b^{4} + a b^{6}\right)} c^{2} d^{7} - 2 \, {\left(4 \, a^{2} b^{5} + 3 \, b^{7}\right)} c d^{8} - {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, a b^{6} c^{9} - 10 \, a^{3} b^{4} c^{7} d^{2} - {\left(a^{2} b^{5} + 3 \, b^{7}\right)} c^{8} d - 3 \, {\left(a^{2} b^{5} + 3 \, b^{7}\right)} c^{6} d^{3} - 6 \, {\left(5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} c^{5} d^{4} - 3 \, {\left(a^{2} b^{5} + 3 \, b^{7}\right)} c^{4} d^{5} - 2 \, {\left(15 \, a^{3} b^{4} + 8 \, a b^{6}\right)} c^{3} d^{6} - {\left(a^{2} b^{5} + 3 \, b^{7}\right)} c^{2} d^{7} - 2 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c d^{8}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(10 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{6} d^{3} - 10 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{5} d^{4} + 3 \, {\left(a^{7} + 5 \, a^{5} b^{2} + 7 \, a^{3} b^{4} + 3 \, a b^{6}\right)} c^{4} d^{5} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} d^{6} - {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{2} d^{7} + {\left(10 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{4} d^{5} - 10 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d^{6} + 3 \, {\left(a^{6} b + 5 \, a^{4} b^{3} + 7 \, a^{2} b^{5} + 3 \, b^{7}\right)} c^{2} d^{7} - 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{8} - {\left(a^{6} b - a^{4} b^{3} - 5 \, a^{2} b^{5} - 3 \, b^{7}\right)} d^{9}\right)} \tan\left(f x + e\right)^{3} + {\left(20 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{5} d^{4} - 10 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{4} d^{5} - 2 \, {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} - 16 \, a^{2} b^{5} - 9 \, b^{7}\right)} c^{3} d^{6} + {\left(3 \, a^{7} + 11 \, a^{5} b^{2} + 13 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{2} d^{7} - 2 \, {\left(2 \, a^{6} b + a^{4} b^{3} - 4 \, a^{2} b^{5} - 3 \, b^{7}\right)} c d^{8} - {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + {\left(10 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{6} d^{3} + 10 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{5} d^{4} - {\left(17 \, a^{6} b + 25 \, a^{4} b^{3} - a^{2} b^{5} - 9 \, b^{7}\right)} c^{4} d^{5} + 2 \, {\left(3 \, a^{7} + 14 \, a^{5} b^{2} + 19 \, a^{3} b^{4} + 8 \, a b^{6}\right)} c^{3} d^{6} - {\left(5 \, a^{6} b + 7 \, a^{4} b^{3} - a^{2} b^{5} - 3 \, b^{7}\right)} c^{2} d^{7} - 2 \, {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c d^{8}\right)} \tan\left(f x + e\right)\right)} \log\left(\frac{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}{\tan\left(f x + e\right)^{2} + 1}\right) - {\left(2 \, a b^{6} c^{9} + 10 \, a b^{6} c^{7} d^{2} - 2 \, {\left(a^{2} b^{5} + 2 \, b^{7}\right)} c^{8} d - 6 \, {\left(a^{2} b^{5} + 2 \, b^{7}\right)} c^{6} d^{3} + 2 \, {\left(5 \, a^{5} b^{2} + 10 \, a^{3} b^{4} + 14 \, a b^{6}\right)} c^{5} d^{4} - {\left(16 \, a^{6} b + 43 \, a^{4} b^{3} + 44 \, a^{2} b^{5} + 23 \, b^{7}\right)} c^{4} d^{5} + 2 \, {\left(3 \, a^{7} + 12 \, a^{5} b^{2} + 15 \, a^{3} b^{4} + 13 \, a b^{6}\right)} c^{3} d^{6} + {\left(5 \, a^{6} b + 5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 9 \, b^{7}\right)} c^{2} d^{7} - 2 \, {\left(3 \, a^{7} + 5 \, a^{5} b^{2} + a^{3} b^{4} - 3 \, a b^{6}\right)} c d^{8} + 3 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{9} + 2 \, {\left(4 \, a^{6} b c d^{8} + {\left(a^{2} b^{5} - b^{7}\right)} c^{9} - 2 \, {\left(a^{3} b^{4} + 2 \, a b^{6}\right)} c^{8} d - {\left(2 \, a^{4} b^{3} - 11 \, a^{2} b^{5} - 3 \, b^{7}\right)} c^{7} d^{2} + 2 \, {\left(4 \, a^{5} b^{2} + 5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} c^{6} d^{3} - {\left(7 \, a^{6} b + 35 \, a^{4} b^{3} + 10 \, a^{2} b^{5}\right)} c^{5} d^{4} + 2 \, {\left(a^{7} + 8 \, a^{5} b^{2} + 10 \, a^{3} b^{4}\right)} c^{4} d^{5} + {\left(9 \, a^{6} b - 5 \, a^{4} b^{3}\right)} c^{3} d^{6} - 2 \, {\left(3 \, a^{7} + 4 \, a^{5} b^{2}\right)} c^{2} d^{7}\right)} f x\right)} \tan\left(f x + e\right)}{2 \, {\left({\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{10} d^{2} - 4 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{9} d^{3} + 3 \, {\left(2 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} c^{8} d^{4} - 4 \, {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c^{7} d^{5} + {\left(a^{8} b + 20 \, a^{6} b^{3} + 40 \, a^{4} b^{5} + 24 \, a^{2} b^{7} + 3 \, b^{9}\right)} c^{6} d^{6} - 12 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d^{7} + {\left(3 \, a^{8} b + 24 \, a^{6} b^{3} + 40 \, a^{4} b^{5} + 20 \, a^{2} b^{7} + b^{9}\right)} c^{4} d^{8} - 4 \, {\left(3 \, a^{7} b^{2} + 7 \, a^{5} b^{4} + 5 \, a^{3} b^{6} + a b^{8}\right)} c^{3} d^{9} + 3 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + 2 \, a^{2} b^{7}\right)} c^{2} d^{10} - 4 \, {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} c d^{11} + {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d^{12}\right)} f \tan\left(f x + e\right)^{3} + {\left(2 \, {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{11} d - 7 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{10} d^{2} + 2 \, {\left(4 \, a^{6} b^{3} + 11 \, a^{4} b^{5} + 10 \, a^{2} b^{7} + 3 \, b^{9}\right)} c^{9} d^{3} - {\left(2 \, a^{7} b^{2} + 25 \, a^{5} b^{4} + 44 \, a^{3} b^{6} + 21 \, a b^{8}\right)} c^{8} d^{4} - 2 \, {\left(a^{8} b - 10 \, a^{6} b^{3} - 26 \, a^{4} b^{5} - 18 \, a^{2} b^{7} - 3 \, b^{9}\right)} c^{7} d^{5} + {\left(a^{9} - 4 \, a^{7} b^{2} - 32 \, a^{5} b^{4} - 48 \, a^{3} b^{6} - 21 \, a b^{8}\right)} c^{6} d^{6} - 2 \, {\left(3 \, a^{8} b - 6 \, a^{6} b^{3} - 22 \, a^{4} b^{5} - 14 \, a^{2} b^{7} - b^{9}\right)} c^{5} d^{7} + {\left(3 \, a^{9} - 16 \, a^{5} b^{4} - 20 \, a^{3} b^{6} - 7 \, a b^{8}\right)} c^{4} d^{8} - 2 \, {\left(3 \, a^{8} b + 2 \, a^{6} b^{3} - 5 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} c^{3} d^{9} + {\left(3 \, a^{9} + 4 \, a^{7} b^{2} - a^{5} b^{4} - 2 \, a^{3} b^{6}\right)} c^{2} d^{10} - 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c d^{11} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d^{12}\right)} f \tan\left(f x + e\right)^{2} + {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{12} - 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{11} d - {\left(2 \, a^{6} b^{3} + a^{4} b^{5} - 4 \, a^{2} b^{7} - 3 \, b^{9}\right)} c^{10} d^{2} + 2 \, {\left(4 \, a^{7} b^{2} + 5 \, a^{5} b^{4} - 2 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{9} d^{3} - {\left(7 \, a^{8} b + 20 \, a^{6} b^{3} + 16 \, a^{4} b^{5} - 3 \, b^{9}\right)} c^{8} d^{4} + 2 \, {\left(a^{9} + 14 \, a^{7} b^{2} + 22 \, a^{5} b^{4} + 6 \, a^{3} b^{6} - 3 \, a b^{8}\right)} c^{7} d^{5} - {\left(21 \, a^{8} b + 48 \, a^{6} b^{3} + 32 \, a^{4} b^{5} + 4 \, a^{2} b^{7} - b^{9}\right)} c^{6} d^{6} + 2 \, {\left(3 \, a^{9} + 18 \, a^{7} b^{2} + 26 \, a^{5} b^{4} + 10 \, a^{3} b^{6} - a b^{8}\right)} c^{5} d^{7} - {\left(21 \, a^{8} b + 44 \, a^{6} b^{3} + 25 \, a^{4} b^{5} + 2 \, a^{2} b^{7}\right)} c^{4} d^{8} + 2 \, {\left(3 \, a^{9} + 10 \, a^{7} b^{2} + 11 \, a^{5} b^{4} + 4 \, a^{3} b^{6}\right)} c^{3} d^{9} - 7 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c^{2} d^{10} + 2 \, {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} c d^{11}\right)} f \tan\left(f x + e\right) + {\left({\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{12} - 4 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{11} d + 3 \, {\left(2 \, a^{7} b^{2} + 5 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} c^{10} d^{2} - 4 \, {\left(a^{8} b + 5 \, a^{6} b^{3} + 7 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} c^{9} d^{3} + {\left(a^{9} + 20 \, a^{7} b^{2} + 40 \, a^{5} b^{4} + 24 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c^{8} d^{4} - 12 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{7} d^{5} + {\left(3 \, a^{9} + 24 \, a^{7} b^{2} + 40 \, a^{5} b^{4} + 20 \, a^{3} b^{6} + a b^{8}\right)} c^{6} d^{6} - 4 \, {\left(3 \, a^{8} b + 7 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{5} d^{7} + 3 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 5 \, a^{5} b^{4} + 2 \, a^{3} b^{6}\right)} c^{4} d^{8} - 4 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c^{3} d^{9} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} c^{2} d^{10}\right)} f\right)}}"," ",0,"-1/2*(2*b^7*c^9 - 2*a*b^6*c^8*d + 6*b^7*c^7*d^2 - 6*a*b^6*c^6*d^3 + 6*b^7*c^5*d^4 + (11*a^5*b^2 + 22*a^3*b^4 + 5*a*b^6)*c^4*d^5 - 2*(9*a^6*b + 18*a^4*b^3 + 9*a^2*b^5 - b^7)*c^3*d^6 + (7*a^7 + 19*a^5*b^2 + 17*a^3*b^4 + 3*a*b^6)*c^2*d^7 - 6*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c*d^8 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^9 - (2*a*b^6*c^7*d^2 - 2*a^2*b^5*c^6*d^3 + 6*a*b^6*c^5*d^4 + 3*(3*a^4*b^3 + 4*a^2*b^5 + 3*b^7)*c^4*d^5 - 2*(7*a^5*b^2 + 14*a^3*b^4 + 4*a*b^6)*c^3*d^6 + (5*a^6*b + 13*a^4*b^3 + 5*a^2*b^5 + 3*b^7)*c^2*d^7 - 2*(a^5*b^2 + 2*a^3*b^4)*c*d^8 - (a^6*b + 2*a^4*b^3 + 3*a^2*b^5)*d^9 + 2*(6*a^5*b^2*c^2*d^7 + 2*a^5*b^2*d^9 + (a^2*b^5 - b^7)*c^7*d^2 - 2*(2*a^3*b^4 + a*b^6)*c^6*d^3 + 3*(2*a^4*b^3 + 5*a^2*b^5 + b^7)*c^5*d^4 - 2*(2*a^5*b^2 + 10*a^3*b^4 + 5*a*b^6)*c^4*d^5 + (a^6*b + 5*a^4*b^3 + 10*a^2*b^5)*c^3*d^6 - (3*a^6*b + 5*a^4*b^3)*c*d^8)*f*x)*tan(f*x + e)^3 - 2*(6*a^6*b*c^4*d^5 + 2*a^6*b*c^2*d^7 + (a^3*b^4 - a*b^6)*c^9 - 2*(2*a^4*b^3 + a^2*b^5)*c^8*d + 3*(2*a^5*b^2 + 5*a^3*b^4 + a*b^6)*c^7*d^2 - 2*(2*a^6*b + 10*a^4*b^3 + 5*a^2*b^5)*c^6*d^3 + (a^7 + 5*a^5*b^2 + 10*a^3*b^4)*c^5*d^4 - (3*a^7 + 5*a^5*b^2)*c^3*d^6)*f*x - (4*a*b^6*c^8*d + 14*a*b^6*c^6*d^3 - 2*(2*a^2*b^5 + b^7)*c^7*d^2 + 2*(5*a^4*b^3 + 4*a^2*b^5 + 2*b^7)*c^5*d^4 - (7*a^5*b^2 + 14*a^3*b^4 - 11*a*b^6)*c^4*d^5 - 2*(4*a^6*b + 11*a^4*b^3 + 16*a^2*b^5 + 6*b^7)*c^3*d^6 + 5*(a^7 + 5*a^5*b^2 + 7*a^3*b^4 + 5*a*b^6)*c^2*d^7 - 2*(4*a^6*b + 10*a^4*b^3 + 10*a^2*b^5 + 3*b^7)*c*d^8 - (a^7 - 2*a^5*b^2 - 7*a^3*b^4 - 6*a*b^6)*d^9 - 2*(10*a^4*b^3*c^2*d^7 - 2*a^6*b*d^9 - 2*(a^2*b^5 - b^7)*c^8*d + (7*a^3*b^4 + 5*a*b^6)*c^7*d^2 - 2*(4*a^4*b^3 + 14*a^2*b^5 + 3*b^7)*c^6*d^3 + (2*a^5*b^2 + 25*a^3*b^4 + 17*a*b^6)*c^5*d^4 + 2*(a^6*b + 5*a^4*b^3 - 5*a^2*b^5)*c^4*d^5 - (a^7 + 17*a^5*b^2 + 10*a^3*b^4)*c^3*d^6 + (3*a^7 + a^5*b^2)*c*d^8)*f*x)*tan(f*x + e)^2 - (2*a^2*b^5*c^9 + 6*a^2*b^5*c^7*d^2 + 6*a^2*b^5*c^5*d^4 + 2*a^2*b^5*c^3*d^6 - (5*a^3*b^4 + 3*a*b^6)*c^8*d - 3*(5*a^3*b^4 + 3*a*b^6)*c^6*d^3 - 3*(5*a^3*b^4 + 3*a*b^6)*c^4*d^5 - (5*a^3*b^4 + 3*a*b^6)*c^2*d^7 + (2*a*b^6*c^7*d^2 + 6*a*b^6*c^5*d^4 + 6*a*b^6*c^3*d^6 + 2*a*b^6*c*d^8 - (5*a^2*b^5 + 3*b^7)*c^6*d^3 - 3*(5*a^2*b^5 + 3*b^7)*c^4*d^5 - 3*(5*a^2*b^5 + 3*b^7)*c^2*d^7 - (5*a^2*b^5 + 3*b^7)*d^9)*tan(f*x + e)^3 + (4*a*b^6*c^8*d - 2*(4*a^2*b^5 + 3*b^7)*c^7*d^2 - (5*a^3*b^4 - 9*a*b^6)*c^6*d^3 - 6*(4*a^2*b^5 + 3*b^7)*c^5*d^4 - 3*(5*a^3*b^4 - a*b^6)*c^4*d^5 - 6*(4*a^2*b^5 + 3*b^7)*c^3*d^6 - 5*(3*a^3*b^4 + a*b^6)*c^2*d^7 - 2*(4*a^2*b^5 + 3*b^7)*c*d^8 - (5*a^3*b^4 + 3*a*b^6)*d^9)*tan(f*x + e)^2 + (2*a*b^6*c^9 - 10*a^3*b^4*c^7*d^2 - (a^2*b^5 + 3*b^7)*c^8*d - 3*(a^2*b^5 + 3*b^7)*c^6*d^3 - 6*(5*a^3*b^4 + 2*a*b^6)*c^5*d^4 - 3*(a^2*b^5 + 3*b^7)*c^4*d^5 - 2*(15*a^3*b^4 + 8*a*b^6)*c^3*d^6 - (a^2*b^5 + 3*b^7)*c^2*d^7 - 2*(5*a^3*b^4 + 3*a*b^6)*c*d^8)*tan(f*x + e))*log((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)/(tan(f*x + e)^2 + 1)) - (10*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^6*d^3 - 10*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c^5*d^4 + 3*(a^7 + 5*a^5*b^2 + 7*a^3*b^4 + 3*a*b^6)*c^4*d^5 - 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c^3*d^6 - (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*c^2*d^7 + (10*(a^4*b^3 + 2*a^2*b^5 + b^7)*c^4*d^5 - 10*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^3*d^6 + 3*(a^6*b + 5*a^4*b^3 + 7*a^2*b^5 + 3*b^7)*c^2*d^7 - 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c*d^8 - (a^6*b - a^4*b^3 - 5*a^2*b^5 - 3*b^7)*d^9)*tan(f*x + e)^3 + (20*(a^4*b^3 + 2*a^2*b^5 + b^7)*c^5*d^4 - 10*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^4*d^5 - 2*(2*a^6*b - 5*a^4*b^3 - 16*a^2*b^5 - 9*b^7)*c^3*d^6 + (3*a^7 + 11*a^5*b^2 + 13*a^3*b^4 + 5*a*b^6)*c^2*d^7 - 2*(2*a^6*b + a^4*b^3 - 4*a^2*b^5 - 3*b^7)*c*d^8 - (a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*d^9)*tan(f*x + e)^2 + (10*(a^4*b^3 + 2*a^2*b^5 + b^7)*c^6*d^3 + 10*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^5*d^4 - (17*a^6*b + 25*a^4*b^3 - a^2*b^5 - 9*b^7)*c^4*d^5 + 2*(3*a^7 + 14*a^5*b^2 + 19*a^3*b^4 + 8*a*b^6)*c^3*d^6 - (5*a^6*b + 7*a^4*b^3 - a^2*b^5 - 3*b^7)*c^2*d^7 - 2*(a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*c*d^8)*tan(f*x + e))*log((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)/(tan(f*x + e)^2 + 1)) - (2*a*b^6*c^9 + 10*a*b^6*c^7*d^2 - 2*(a^2*b^5 + 2*b^7)*c^8*d - 6*(a^2*b^5 + 2*b^7)*c^6*d^3 + 2*(5*a^5*b^2 + 10*a^3*b^4 + 14*a*b^6)*c^5*d^4 - (16*a^6*b + 43*a^4*b^3 + 44*a^2*b^5 + 23*b^7)*c^4*d^5 + 2*(3*a^7 + 12*a^5*b^2 + 15*a^3*b^4 + 13*a*b^6)*c^3*d^6 + (5*a^6*b + 5*a^4*b^3 - 7*a^2*b^5 - 9*b^7)*c^2*d^7 - 2*(3*a^7 + 5*a^5*b^2 + a^3*b^4 - 3*a*b^6)*c*d^8 + 3*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d^9 + 2*(4*a^6*b*c*d^8 + (a^2*b^5 - b^7)*c^9 - 2*(a^3*b^4 + 2*a*b^6)*c^8*d - (2*a^4*b^3 - 11*a^2*b^5 - 3*b^7)*c^7*d^2 + 2*(4*a^5*b^2 + 5*a^3*b^4 - 2*a*b^6)*c^6*d^3 - (7*a^6*b + 35*a^4*b^3 + 10*a^2*b^5)*c^5*d^4 + 2*(a^7 + 8*a^5*b^2 + 10*a^3*b^4)*c^4*d^5 + (9*a^6*b - 5*a^4*b^3)*c^3*d^6 - 2*(3*a^7 + 4*a^5*b^2)*c^2*d^7)*f*x)*tan(f*x + e))/(((a^4*b^5 + 2*a^2*b^7 + b^9)*c^10*d^2 - 4*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^9*d^3 + 3*(2*a^6*b^3 + 5*a^4*b^5 + 4*a^2*b^7 + b^9)*c^8*d^4 - 4*(a^7*b^2 + 5*a^5*b^4 + 7*a^3*b^6 + 3*a*b^8)*c^7*d^5 + (a^8*b + 20*a^6*b^3 + 40*a^4*b^5 + 24*a^2*b^7 + 3*b^9)*c^6*d^6 - 12*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^5*d^7 + (3*a^8*b + 24*a^6*b^3 + 40*a^4*b^5 + 20*a^2*b^7 + b^9)*c^4*d^8 - 4*(3*a^7*b^2 + 7*a^5*b^4 + 5*a^3*b^6 + a*b^8)*c^3*d^9 + 3*(a^8*b + 4*a^6*b^3 + 5*a^4*b^5 + 2*a^2*b^7)*c^2*d^10 - 4*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*c*d^11 + (a^8*b + 2*a^6*b^3 + a^4*b^5)*d^12)*f*tan(f*x + e)^3 + (2*(a^4*b^5 + 2*a^2*b^7 + b^9)*c^11*d - 7*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^10*d^2 + 2*(4*a^6*b^3 + 11*a^4*b^5 + 10*a^2*b^7 + 3*b^9)*c^9*d^3 - (2*a^7*b^2 + 25*a^5*b^4 + 44*a^3*b^6 + 21*a*b^8)*c^8*d^4 - 2*(a^8*b - 10*a^6*b^3 - 26*a^4*b^5 - 18*a^2*b^7 - 3*b^9)*c^7*d^5 + (a^9 - 4*a^7*b^2 - 32*a^5*b^4 - 48*a^3*b^6 - 21*a*b^8)*c^6*d^6 - 2*(3*a^8*b - 6*a^6*b^3 - 22*a^4*b^5 - 14*a^2*b^7 - b^9)*c^5*d^7 + (3*a^9 - 16*a^5*b^4 - 20*a^3*b^6 - 7*a*b^8)*c^4*d^8 - 2*(3*a^8*b + 2*a^6*b^3 - 5*a^4*b^5 - 4*a^2*b^7)*c^3*d^9 + (3*a^9 + 4*a^7*b^2 - a^5*b^4 - 2*a^3*b^6)*c^2*d^10 - 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c*d^11 + (a^9 + 2*a^7*b^2 + a^5*b^4)*d^12)*f*tan(f*x + e)^2 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^12 - 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^11*d - (2*a^6*b^3 + a^4*b^5 - 4*a^2*b^7 - 3*b^9)*c^10*d^2 + 2*(4*a^7*b^2 + 5*a^5*b^4 - 2*a^3*b^6 - 3*a*b^8)*c^9*d^3 - (7*a^8*b + 20*a^6*b^3 + 16*a^4*b^5 - 3*b^9)*c^8*d^4 + 2*(a^9 + 14*a^7*b^2 + 22*a^5*b^4 + 6*a^3*b^6 - 3*a*b^8)*c^7*d^5 - (21*a^8*b + 48*a^6*b^3 + 32*a^4*b^5 + 4*a^2*b^7 - b^9)*c^6*d^6 + 2*(3*a^9 + 18*a^7*b^2 + 26*a^5*b^4 + 10*a^3*b^6 - a*b^8)*c^5*d^7 - (21*a^8*b + 44*a^6*b^3 + 25*a^4*b^5 + 2*a^2*b^7)*c^4*d^8 + 2*(3*a^9 + 10*a^7*b^2 + 11*a^5*b^4 + 4*a^3*b^6)*c^3*d^9 - 7*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^2*d^10 + 2*(a^9 + 2*a^7*b^2 + a^5*b^4)*c*d^11)*f*tan(f*x + e) + ((a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^12 - 4*(a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c^11*d + 3*(2*a^7*b^2 + 5*a^5*b^4 + 4*a^3*b^6 + a*b^8)*c^10*d^2 - 4*(a^8*b + 5*a^6*b^3 + 7*a^4*b^5 + 3*a^2*b^7)*c^9*d^3 + (a^9 + 20*a^7*b^2 + 40*a^5*b^4 + 24*a^3*b^6 + 3*a*b^8)*c^8*d^4 - 12*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c^7*d^5 + (3*a^9 + 24*a^7*b^2 + 40*a^5*b^4 + 20*a^3*b^6 + a*b^8)*c^6*d^6 - 4*(3*a^8*b + 7*a^6*b^3 + 5*a^4*b^5 + a^2*b^7)*c^5*d^7 + 3*(a^9 + 4*a^7*b^2 + 5*a^5*b^4 + 2*a^3*b^6)*c^4*d^8 - 4*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^3*d^9 + (a^9 + 2*a^7*b^2 + a^5*b^4)*c^2*d^10)*f)","B",0
1229,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,1,8608,0,19.806334," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} f^{5} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c^{3} + {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{2} d + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c d^{2} + {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{3}\right)} f^{4} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left(2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{4} + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c^{3} d + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c d^{3}\right)} f^{2} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + \sqrt{2} {\left({\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c + {\left(a^{4} b - b^{5}\right)} d\right)} f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left(2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{2} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} c d + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{2}\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}}\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left(b f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left({\left(a^{2} b + b^{3}\right)} c + {\left(a^{3} + a b^{2}\right)} d\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}}\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} + 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) + \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{3} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d + {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} c d^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)} f^{3} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{4} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c^{3} d + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c d^{3} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{4}\right)} f \cos\left(f x + e\right)\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{5} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{4} d + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{3} d^{2} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d^{3} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{4} d + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{3} d^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} d^{3} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{4} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{5}\right)} \sin\left(f x + e\right)}{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{3}{4}}}{4 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{4} d + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} c^{3} d^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{2} d^{3} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} c d^{4} + {\left(a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d^{5}}\right) + 4 \, \sqrt{2} f^{5} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c^{3} + {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{2} d + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c d^{2} + {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{3}\right)} f^{4} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left(2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{4} + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c^{3} d + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} + {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c d^{3}\right)} f^{2} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - \sqrt{2} {\left({\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c + {\left(a^{4} b - b^{5}\right)} d\right)} f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left(2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{2} + {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} c d + {\left(a^{7} + a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} d^{2}\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}}\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left(b f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left({\left(a^{2} b + b^{3}\right)} c + {\left(a^{3} + a b^{2}\right)} d\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}}\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} + 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) - \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{3} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d + {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} c d^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)} f^{3} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{4} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c^{3} d + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c d^{3} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{4}\right)} f \cos\left(f x + e\right)\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{5} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{4} d + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{3} d^{2} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d^{3} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{4} d + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{3} d^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} d^{3} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{4} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{5}\right)} \sin\left(f x + e\right)}{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{3}{4}}}{4 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{4} d + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} c^{3} d^{2} + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{2} d^{3} + 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} c d^{4} + {\left(a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d^{5}}\right) - \sqrt{2} {\left({\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{3} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} f\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} + 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) + \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{3} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d + {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} c d^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)} f^{3} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{4} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c^{3} d + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c d^{3} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{4}\right)} f \cos\left(f x + e\right)\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{5} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{4} d + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{3} d^{2} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d^{3} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{4} d + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{3} d^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} d^{3} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{4} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{5}\right)} \sin\left(f x + e\right)}{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)}\right) + \sqrt{2} {\left({\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{3} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} f\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} + 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) - \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{3} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d + {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} c d^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)} f^{3} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{4} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c^{3} d + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} c^{2} d^{2} + 4 \, {\left(a^{5} b^{2} - a b^{6}\right)} c d^{3} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{4}\right)} f \cos\left(f x + e\right)\right)} \sqrt{-\frac{{\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{5} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{4} d + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{3} d^{2} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d^{3} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{4} d + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{3} d^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} d^{3} + 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{4} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{5}\right)} \sin\left(f x + e\right)}{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)}\right) + 8 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} f}"," ",0,"1/4*(4*sqrt(2)*f^5*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(3/4)*arctan(((2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c^3 + (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^2*d + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c*d^2 + (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^3)*f^4*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + (2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^4 + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c^3*d + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c*d^3)*f^2*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4) + sqrt(2)*((2*(a^3*b^2 + a*b^4)*c + (a^4*b - b^5)*d)*f^7*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + (2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^2 + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*c*d + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^2)*f^5*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(3/4) + sqrt(2)*(b*f^7*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + ((a^2*b + b^3)*c + (a^3 + a*b^2)*d)*f^5*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt(((4*(a^4*b^2 + a^2*b^4)*c^4 + 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) + sqrt(2)*((4*a^2*b^3*c^3 + 4*(2*a^3*b^2 - a*b^4)*c^2*d + (5*a^4*b - 6*a^2*b^3 + b^5)*c*d^2 + (a^5 - 2*a^3*b^2 + a*b^4)*d^3)*f^3*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^4 + 4*(a^5*b^2 - a*b^6)*c^3*d + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*c^2*d^2 + 4*(a^5*b^2 - a*b^6)*c*d^3 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^4)*f*cos(f*x + e))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^5 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^4*d + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^3*d^2 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d^3 + (a^8 - 2*a^4*b^4 + b^8)*c*d^4)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^4*d + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^3*d^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2*d^3 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^4 + (a^8 - 2*a^4*b^4 + b^8)*d^5)*sin(f*x + e))/((c^2 + d^2)*cos(f*x + e)))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(3/4))/(4*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*c^4*d + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*c^3*d^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*c^2*d^3 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*c*d^4 + (a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)*d^5)) + 4*sqrt(2)*f^5*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(3/4)*arctan(-((2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c^3 + (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^2*d + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c*d^2 + (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^3)*f^4*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + (2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^4 + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c^3*d + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 + (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c*d^3)*f^2*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4) - sqrt(2)*((2*(a^3*b^2 + a*b^4)*c + (a^4*b - b^5)*d)*f^7*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + (2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^2 + (3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*c*d + (a^7 + a^5*b^2 - a^3*b^4 - a*b^6)*d^2)*f^5*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(3/4) - sqrt(2)*(b*f^7*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4)*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + ((a^2*b + b^3)*c + (a^3 + a*b^2)*d)*f^5*sqrt((4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/f^4))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt(((4*(a^4*b^2 + a^2*b^4)*c^4 + 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) - sqrt(2)*((4*a^2*b^3*c^3 + 4*(2*a^3*b^2 - a*b^4)*c^2*d + (5*a^4*b - 6*a^2*b^3 + b^5)*c*d^2 + (a^5 - 2*a^3*b^2 + a*b^4)*d^3)*f^3*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^4 + 4*(a^5*b^2 - a*b^6)*c^3*d + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*c^2*d^2 + 4*(a^5*b^2 - a*b^6)*c*d^3 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^4)*f*cos(f*x + e))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^5 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^4*d + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^3*d^2 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d^3 + (a^8 - 2*a^4*b^4 + b^8)*c*d^4)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^4*d + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^3*d^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2*d^3 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^4 + (a^8 - 2*a^4*b^4 + b^8)*d^5)*sin(f*x + e))/((c^2 + d^2)*cos(f*x + e)))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(3/4))/(4*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*c^4*d + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*c^3*d^2 + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*c^2*d^3 + 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*c*d^4 + (a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)*d^5)) - sqrt(2)*((2*a*b*d - (a^2 - b^2)*c)*f^3*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + ((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*f)*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(1/4)*log(((4*(a^4*b^2 + a^2*b^4)*c^4 + 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) + sqrt(2)*((4*a^2*b^3*c^3 + 4*(2*a^3*b^2 - a*b^4)*c^2*d + (5*a^4*b - 6*a^2*b^3 + b^5)*c*d^2 + (a^5 - 2*a^3*b^2 + a*b^4)*d^3)*f^3*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^4 + 4*(a^5*b^2 - a*b^6)*c^3*d + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*c^2*d^2 + 4*(a^5*b^2 - a*b^6)*c*d^3 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^4)*f*cos(f*x + e))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^5 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^4*d + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^3*d^2 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d^3 + (a^8 - 2*a^4*b^4 + b^8)*c*d^4)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^4*d + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^3*d^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2*d^3 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^4 + (a^8 - 2*a^4*b^4 + b^8)*d^5)*sin(f*x + e))/((c^2 + d^2)*cos(f*x + e))) + sqrt(2)*((2*a*b*d - (a^2 - b^2)*c)*f^3*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) + ((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*f)*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(1/4)*log(((4*(a^4*b^2 + a^2*b^4)*c^4 + 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) - sqrt(2)*((4*a^2*b^3*c^3 + 4*(2*a^3*b^2 - a*b^4)*c^2*d + (5*a^4*b - 6*a^2*b^3 + b^5)*c*d^2 + (a^5 - 2*a^3*b^2 + a*b^4)*d^3)*f^3*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^4 + 4*(a^5*b^2 - a*b^6)*c^3*d + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*c^2*d^2 + 4*(a^5*b^2 - a*b^6)*c*d^3 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^4)*f*cos(f*x + e))*sqrt(-((2*a*b*d - (a^2 - b^2)*c)*f^2*sqrt(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4) - (a^4 + 2*a^2*b^2 + b^4)*c^2 - (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 + 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/f^4)^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^5 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^4*d + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^3*d^2 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d^3 + (a^8 - 2*a^4*b^4 + b^8)*c*d^4)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^4*d + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^3*d^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2*d^3 + 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^4 + (a^8 - 2*a^4*b^4 + b^8)*d^5)*sin(f*x + e))/((c^2 + d^2)*cos(f*x + e))) + 8*((a^4*b + 2*a^2*b^3 + b^5)*c^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2)*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)))/(((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*f)","B",0
1232,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1234,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1235,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1237,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1238,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1243,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1244,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1245,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1246,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1248,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,1,14923,0,164.746028," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(c^{2} d + d^{3}\right)} f^{5} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(4 \, {\left(a^{15} b + 5 \, a^{13} b^{3} + 9 \, a^{11} b^{5} + 5 \, a^{9} b^{7} - 5 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 5 \, a^{3} b^{13} - a b^{15}\right)} c^{5} - {\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} c^{4} d + 8 \, {\left(a^{15} b + 5 \, a^{13} b^{3} + 9 \, a^{11} b^{5} + 5 \, a^{9} b^{7} - 5 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 5 \, a^{3} b^{13} - a b^{15}\right)} c^{3} d^{2} - 2 \, {\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} c^{2} d^{3} + 4 \, {\left(a^{15} b + 5 \, a^{13} b^{3} + 9 \, a^{11} b^{5} + 5 \, a^{9} b^{7} - 5 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 5 \, a^{3} b^{13} - a b^{15}\right)} c d^{4} - {\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{5}\right)} f^{4} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(4 \, {\left(a^{19} b + 7 \, a^{17} b^{3} + 20 \, a^{15} b^{5} + 28 \, a^{13} b^{7} + 14 \, a^{11} b^{9} - 14 \, a^{9} b^{11} - 28 \, a^{7} b^{13} - 20 \, a^{5} b^{15} - 7 \, a^{3} b^{17} - a b^{19}\right)} c^{4} - {\left(a^{20} + 2 \, a^{18} b^{2} - 19 \, a^{16} b^{4} - 104 \, a^{14} b^{6} - 238 \, a^{12} b^{8} - 308 \, a^{10} b^{10} - 238 \, a^{8} b^{12} - 104 \, a^{6} b^{14} - 19 \, a^{4} b^{16} + 2 \, a^{2} b^{18} + b^{20}\right)} c^{3} d + 4 \, {\left(a^{19} b + 7 \, a^{17} b^{3} + 20 \, a^{15} b^{5} + 28 \, a^{13} b^{7} + 14 \, a^{11} b^{9} - 14 \, a^{9} b^{11} - 28 \, a^{7} b^{13} - 20 \, a^{5} b^{15} - 7 \, a^{3} b^{17} - a b^{19}\right)} c^{2} d^{2} - {\left(a^{20} + 2 \, a^{18} b^{2} - 19 \, a^{16} b^{4} - 104 \, a^{14} b^{6} - 238 \, a^{12} b^{8} - 308 \, a^{10} b^{10} - 238 \, a^{8} b^{12} - 104 \, a^{6} b^{14} - 19 \, a^{4} b^{16} + 2 \, a^{2} b^{18} + b^{20}\right)} c d^{3}\right)} f^{2} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} + \sqrt{2} {\left({\left(2 \, a b c^{5} + 4 \, a b c^{3} d^{2} + 2 \, a b c d^{4} - {\left(a^{2} - b^{2}\right)} c^{4} d - 2 \, {\left(a^{2} - b^{2}\right)} c^{2} d^{3} - {\left(a^{2} - b^{2}\right)} d^{5}\right)} f^{7} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + 2 \, {\left({\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c^{2} d^{2} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{4}\right)} f^{5} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{{\left(16 \, {\left(a^{10} b^{2} - 2 \, a^{6} b^{6} + a^{2} b^{10}\right)} c^{4} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c^{3} d + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{2} d^{2} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c d^{3} + {\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} {\left(2 \, {\left(16 \, {\left(a^{7} b^{3} - 2 \, a^{5} b^{5} + a^{3} b^{7}\right)} c^{4} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c^{3} d + {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c d^{3} + {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(32 \, {\left(a^{11} b^{3} - 2 \, a^{7} b^{7} + a^{3} b^{11}\right)} c^{3} - 32 \, {\left(a^{12} b^{2} - 3 \, a^{10} b^{4} - 4 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{2} d + 2 \, {\left(5 \, a^{13} b - 34 \, a^{11} b^{3} + 11 \, a^{9} b^{5} + 100 \, a^{7} b^{7} + 11 \, a^{5} b^{9} - 34 \, a^{3} b^{11} + 5 \, a b^{13}\right)} c d^{2} - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{3} - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c^{2} d + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{2} d - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c d^{2} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(8 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} c^{6} - 2 \, {\left(3 \, a^{9} b - 4 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + 3 \, a b^{9}\right)} c^{5} d + {\left(a^{10} + 11 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} - 11 \, a^{2} b^{8} - b^{10}\right)} c^{4} d^{2} - 4 \, {\left(3 \, a^{9} b - 4 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + 3 \, a b^{9}\right)} c^{3} d^{3} + 2 \, {\left(a^{10} - a^{8} b^{2} - 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} + a^{2} b^{8} - b^{10}\right)} c^{2} d^{4} - 2 \, {\left(3 \, a^{9} b - 4 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + 3 \, a b^{9}\right)} c d^{5} + {\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{6}\right)} f^{7} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + 2 \, {\left(4 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 2 \, a^{6} b^{8} - 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{5} - {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} c^{4} d + 8 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 2 \, a^{6} b^{8} - 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{3} d^{2} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} c^{2} d^{3} + 4 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 2 \, a^{6} b^{8} - 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c d^{4} - {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5}\right)} f^{5} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}}}{16 \, {\left(a^{22} b^{2} + 6 \, a^{20} b^{4} + 13 \, a^{18} b^{6} + 8 \, a^{16} b^{8} - 14 \, a^{14} b^{10} - 28 \, a^{12} b^{12} - 14 \, a^{10} b^{14} + 8 \, a^{8} b^{16} + 13 \, a^{6} b^{18} + 6 \, a^{4} b^{20} + a^{2} b^{22}\right)} c^{2} d - 8 \, {\left(a^{23} b + a^{21} b^{3} - 21 \, a^{19} b^{5} - 85 \, a^{17} b^{7} - 134 \, a^{15} b^{9} - 70 \, a^{13} b^{11} + 70 \, a^{11} b^{13} + 134 \, a^{9} b^{15} + 85 \, a^{7} b^{17} + 21 \, a^{5} b^{19} - a^{3} b^{21} - a b^{23}\right)} c d^{2} + {\left(a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}\right)} d^{3}}\right) + 4 \, \sqrt{2} {\left(c^{2} d + d^{3}\right)} f^{5} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(4 \, {\left(a^{15} b + 5 \, a^{13} b^{3} + 9 \, a^{11} b^{5} + 5 \, a^{9} b^{7} - 5 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 5 \, a^{3} b^{13} - a b^{15}\right)} c^{5} - {\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} c^{4} d + 8 \, {\left(a^{15} b + 5 \, a^{13} b^{3} + 9 \, a^{11} b^{5} + 5 \, a^{9} b^{7} - 5 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 5 \, a^{3} b^{13} - a b^{15}\right)} c^{3} d^{2} - 2 \, {\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} c^{2} d^{3} + 4 \, {\left(a^{15} b + 5 \, a^{13} b^{3} + 9 \, a^{11} b^{5} + 5 \, a^{9} b^{7} - 5 \, a^{7} b^{9} - 9 \, a^{5} b^{11} - 5 \, a^{3} b^{13} - a b^{15}\right)} c d^{4} - {\left(a^{16} - 20 \, a^{12} b^{4} - 64 \, a^{10} b^{6} - 90 \, a^{8} b^{8} - 64 \, a^{6} b^{10} - 20 \, a^{4} b^{12} + b^{16}\right)} d^{5}\right)} f^{4} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(4 \, {\left(a^{19} b + 7 \, a^{17} b^{3} + 20 \, a^{15} b^{5} + 28 \, a^{13} b^{7} + 14 \, a^{11} b^{9} - 14 \, a^{9} b^{11} - 28 \, a^{7} b^{13} - 20 \, a^{5} b^{15} - 7 \, a^{3} b^{17} - a b^{19}\right)} c^{4} - {\left(a^{20} + 2 \, a^{18} b^{2} - 19 \, a^{16} b^{4} - 104 \, a^{14} b^{6} - 238 \, a^{12} b^{8} - 308 \, a^{10} b^{10} - 238 \, a^{8} b^{12} - 104 \, a^{6} b^{14} - 19 \, a^{4} b^{16} + 2 \, a^{2} b^{18} + b^{20}\right)} c^{3} d + 4 \, {\left(a^{19} b + 7 \, a^{17} b^{3} + 20 \, a^{15} b^{5} + 28 \, a^{13} b^{7} + 14 \, a^{11} b^{9} - 14 \, a^{9} b^{11} - 28 \, a^{7} b^{13} - 20 \, a^{5} b^{15} - 7 \, a^{3} b^{17} - a b^{19}\right)} c^{2} d^{2} - {\left(a^{20} + 2 \, a^{18} b^{2} - 19 \, a^{16} b^{4} - 104 \, a^{14} b^{6} - 238 \, a^{12} b^{8} - 308 \, a^{10} b^{10} - 238 \, a^{8} b^{12} - 104 \, a^{6} b^{14} - 19 \, a^{4} b^{16} + 2 \, a^{2} b^{18} + b^{20}\right)} c d^{3}\right)} f^{2} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} - \sqrt{2} {\left({\left(2 \, a b c^{5} + 4 \, a b c^{3} d^{2} + 2 \, a b c d^{4} - {\left(a^{2} - b^{2}\right)} c^{4} d - 2 \, {\left(a^{2} - b^{2}\right)} c^{2} d^{3} - {\left(a^{2} - b^{2}\right)} d^{5}\right)} f^{7} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + 2 \, {\left({\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c^{4} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c^{2} d^{2} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d^{4}\right)} f^{5} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{{\left(16 \, {\left(a^{10} b^{2} - 2 \, a^{6} b^{6} + a^{2} b^{10}\right)} c^{4} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c^{3} d + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{2} d^{2} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c d^{3} + {\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} {\left(2 \, {\left(16 \, {\left(a^{7} b^{3} - 2 \, a^{5} b^{5} + a^{3} b^{7}\right)} c^{4} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c^{3} d + {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c d^{3} + {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(32 \, {\left(a^{11} b^{3} - 2 \, a^{7} b^{7} + a^{3} b^{11}\right)} c^{3} - 32 \, {\left(a^{12} b^{2} - 3 \, a^{10} b^{4} - 4 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{2} d + 2 \, {\left(5 \, a^{13} b - 34 \, a^{11} b^{3} + 11 \, a^{9} b^{5} + 100 \, a^{7} b^{7} + 11 \, a^{5} b^{9} - 34 \, a^{3} b^{11} + 5 \, a b^{13}\right)} c d^{2} - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{3} - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c^{2} d + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{2} d - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c d^{2} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(8 \, {\left(a^{8} b^{2} + a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8}\right)} c^{6} - 2 \, {\left(3 \, a^{9} b - 4 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + 3 \, a b^{9}\right)} c^{5} d + {\left(a^{10} + 11 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} - 11 \, a^{2} b^{8} - b^{10}\right)} c^{4} d^{2} - 4 \, {\left(3 \, a^{9} b - 4 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + 3 \, a b^{9}\right)} c^{3} d^{3} + 2 \, {\left(a^{10} - a^{8} b^{2} - 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} + a^{2} b^{8} - b^{10}\right)} c^{2} d^{4} - 2 \, {\left(3 \, a^{9} b - 4 \, a^{7} b^{3} - 14 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + 3 \, a b^{9}\right)} c d^{5} + {\left(a^{10} - 5 \, a^{8} b^{2} - 6 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} d^{6}\right)} f^{7} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + 2 \, {\left(4 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 2 \, a^{6} b^{8} - 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{5} - {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} c^{4} d + 8 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 2 \, a^{6} b^{8} - 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{3} d^{2} - 2 \, {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} c^{2} d^{3} + 4 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 2 \, a^{6} b^{8} - 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c d^{4} - {\left(a^{13} b - 2 \, a^{11} b^{3} - 17 \, a^{9} b^{5} - 28 \, a^{7} b^{7} - 17 \, a^{5} b^{9} - 2 \, a^{3} b^{11} + a b^{13}\right)} d^{5}\right)} f^{5} \sqrt{\frac{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}}}{16 \, {\left(a^{22} b^{2} + 6 \, a^{20} b^{4} + 13 \, a^{18} b^{6} + 8 \, a^{16} b^{8} - 14 \, a^{14} b^{10} - 28 \, a^{12} b^{12} - 14 \, a^{10} b^{14} + 8 \, a^{8} b^{16} + 13 \, a^{6} b^{18} + 6 \, a^{4} b^{20} + a^{2} b^{22}\right)} c^{2} d - 8 \, {\left(a^{23} b + a^{21} b^{3} - 21 \, a^{19} b^{5} - 85 \, a^{17} b^{7} - 134 \, a^{15} b^{9} - 70 \, a^{13} b^{11} + 70 \, a^{11} b^{13} + 134 \, a^{9} b^{15} + 85 \, a^{7} b^{17} + 21 \, a^{5} b^{19} - a^{3} b^{21} - a b^{23}\right)} c d^{2} + {\left(a^{24} - 4 \, a^{22} b^{2} - 30 \, a^{20} b^{4} + 12 \, a^{18} b^{6} + 367 \, a^{16} b^{8} + 1016 \, a^{14} b^{10} + 1372 \, a^{12} b^{12} + 1016 \, a^{10} b^{14} + 367 \, a^{8} b^{16} + 12 \, a^{6} b^{18} - 30 \, a^{4} b^{20} - 4 \, a^{2} b^{22} + b^{24}\right)} d^{3}}\right) + \sqrt{2} {\left({\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2}\right)} f^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d f\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(16 \, {\left(a^{10} b^{2} - 2 \, a^{6} b^{6} + a^{2} b^{10}\right)} c^{4} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c^{3} d + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{2} d^{2} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c d^{3} + {\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} {\left(2 \, {\left(16 \, {\left(a^{7} b^{3} - 2 \, a^{5} b^{5} + a^{3} b^{7}\right)} c^{4} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c^{3} d + {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c d^{3} + {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(32 \, {\left(a^{11} b^{3} - 2 \, a^{7} b^{7} + a^{3} b^{11}\right)} c^{3} - 32 \, {\left(a^{12} b^{2} - 3 \, a^{10} b^{4} - 4 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{2} d + 2 \, {\left(5 \, a^{13} b - 34 \, a^{11} b^{3} + 11 \, a^{9} b^{5} + 100 \, a^{7} b^{7} + 11 \, a^{5} b^{9} - 34 \, a^{3} b^{11} + 5 \, a b^{13}\right)} c d^{2} - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{3} - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c^{2} d + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{2} d - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c d^{2} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - \sqrt{2} {\left({\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{2}\right)} f^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d f\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(16 \, {\left(a^{10} b^{2} - 2 \, a^{6} b^{6} + a^{2} b^{10}\right)} c^{4} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c^{3} d + {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} c^{2} d^{2} - 8 \, {\left(a^{11} b - 5 \, a^{9} b^{3} - 6 \, a^{7} b^{5} + 6 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} c d^{3} + {\left(a^{12} - 10 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 52 \, a^{6} b^{6} + 15 \, a^{4} b^{8} - 10 \, a^{2} b^{10} + b^{12}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} {\left(2 \, {\left(16 \, {\left(a^{7} b^{3} - 2 \, a^{5} b^{5} + a^{3} b^{7}\right)} c^{4} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c^{3} d + {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} - 8 \, {\left(a^{8} b^{2} - 7 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - a^{2} b^{8}\right)} c d^{3} + {\left(a^{9} b - 12 \, a^{7} b^{3} + 38 \, a^{5} b^{5} - 12 \, a^{3} b^{7} + a b^{9}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(32 \, {\left(a^{11} b^{3} - 2 \, a^{7} b^{7} + a^{3} b^{11}\right)} c^{3} - 32 \, {\left(a^{12} b^{2} - 3 \, a^{10} b^{4} - 4 \, a^{8} b^{6} + 4 \, a^{6} b^{8} + 3 \, a^{4} b^{10} - a^{2} b^{12}\right)} c^{2} d + 2 \, {\left(5 \, a^{13} b - 34 \, a^{11} b^{3} + 11 \, a^{9} b^{5} + 100 \, a^{7} b^{7} + 11 \, a^{5} b^{9} - 34 \, a^{3} b^{11} + 5 \, a b^{13}\right)} c d^{2} - {\left(a^{14} - 11 \, a^{12} b^{2} + 25 \, a^{10} b^{4} + 37 \, a^{8} b^{6} - 37 \, a^{6} b^{8} - 25 \, a^{4} b^{10} + 11 \, a^{2} b^{12} - b^{14}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 4 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} f^{2} \sqrt{\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} c^{2} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}{16 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 8 \, {\left(a^{7} b - 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} - a b^{7}\right)} c d + {\left(a^{8} - 12 \, a^{6} b^{2} + 38 \, a^{4} b^{4} - 12 \, a^{2} b^{6} + b^{8}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{3} - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c^{2} d + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(16 \, {\left(a^{14} b^{2} + 2 \, a^{12} b^{4} - a^{10} b^{6} - 4 \, a^{8} b^{8} - a^{6} b^{10} + 2 \, a^{4} b^{12} + a^{2} b^{14}\right)} c^{2} d - 8 \, {\left(a^{15} b - 3 \, a^{13} b^{3} - 15 \, a^{11} b^{5} - 11 \, a^{9} b^{7} + 11 \, a^{7} b^{9} + 15 \, a^{5} b^{11} + 3 \, a^{3} b^{13} - a b^{15}\right)} c d^{2} + {\left(a^{16} - 8 \, a^{14} b^{2} - 4 \, a^{12} b^{4} + 72 \, a^{10} b^{6} + 134 \, a^{8} b^{8} + 72 \, a^{6} b^{10} - 4 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 8 \, {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{4 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d f}"," ",0,"1/4*(4*sqrt(2)*(c^2*d + d^3)*f^5*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(3/4)*arctan(((4*(a^15*b + 5*a^13*b^3 + 9*a^11*b^5 + 5*a^9*b^7 - 5*a^7*b^9 - 9*a^5*b^11 - 5*a^3*b^13 - a*b^15)*c^5 - (a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*c^4*d + 8*(a^15*b + 5*a^13*b^3 + 9*a^11*b^5 + 5*a^9*b^7 - 5*a^7*b^9 - 9*a^5*b^11 - 5*a^3*b^13 - a*b^15)*c^3*d^2 - 2*(a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*c^2*d^3 + 4*(a^15*b + 5*a^13*b^3 + 9*a^11*b^5 + 5*a^9*b^7 - 5*a^7*b^9 - 9*a^5*b^11 - 5*a^3*b^13 - a*b^15)*c*d^4 - (a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^5)*f^4*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (4*(a^19*b + 7*a^17*b^3 + 20*a^15*b^5 + 28*a^13*b^7 + 14*a^11*b^9 - 14*a^9*b^11 - 28*a^7*b^13 - 20*a^5*b^15 - 7*a^3*b^17 - a*b^19)*c^4 - (a^20 + 2*a^18*b^2 - 19*a^16*b^4 - 104*a^14*b^6 - 238*a^12*b^8 - 308*a^10*b^10 - 238*a^8*b^12 - 104*a^6*b^14 - 19*a^4*b^16 + 2*a^2*b^18 + b^20)*c^3*d + 4*(a^19*b + 7*a^17*b^3 + 20*a^15*b^5 + 28*a^13*b^7 + 14*a^11*b^9 - 14*a^9*b^11 - 28*a^7*b^13 - 20*a^5*b^15 - 7*a^3*b^17 - a*b^19)*c^2*d^2 - (a^20 + 2*a^18*b^2 - 19*a^16*b^4 - 104*a^14*b^6 - 238*a^12*b^8 - 308*a^10*b^10 - 238*a^8*b^12 - 104*a^6*b^14 - 19*a^4*b^16 + 2*a^2*b^18 + b^20)*c*d^3)*f^2*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)) + sqrt(2)*((2*a*b*c^5 + 4*a*b*c^3*d^2 + 2*a*b*c*d^4 - (a^2 - b^2)*c^4*d - 2*(a^2 - b^2)*c^2*d^3 - (a^2 - b^2)*d^5)*f^7*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + 2*((a^5*b + 2*a^3*b^3 + a*b^5)*c^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*c^2*d^2 + (a^5*b + 2*a^3*b^3 + a*b^5)*d^4)*f^5*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt(((16*(a^10*b^2 - 2*a^6*b^6 + a^2*b^10)*c^4 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c^3*d + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*c^2*d^2 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c*d^3 + (a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^4)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) + sqrt(2)*(2*(16*(a^7*b^3 - 2*a^5*b^5 + a^3*b^7)*c^4 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c^3*d + (a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c*d^3 + (a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^4)*f^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) + (32*(a^11*b^3 - 2*a^7*b^7 + a^3*b^11)*c^3 - 32*(a^12*b^2 - 3*a^10*b^4 - 4*a^8*b^6 + 4*a^6*b^8 + 3*a^4*b^10 - a^2*b^12)*c^2*d + 2*(5*a^13*b - 34*a^11*b^3 + 11*a^9*b^5 + 100*a^7*b^7 + 11*a^5*b^9 - 34*a^3*b^11 + 5*a*b^13)*c*d^2 - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3)*f*cos(f*x + e))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(1/4) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^3 - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c^2*d + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*c*d^2)*cos(f*x + e) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^2*d - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c*d^2 + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*d^3)*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(3/4) + sqrt(2)*((8*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*c^6 - 2*(3*a^9*b - 4*a^7*b^3 - 14*a^5*b^5 - 4*a^3*b^7 + 3*a*b^9)*c^5*d + (a^10 + 11*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 - 11*a^2*b^8 - b^10)*c^4*d^2 - 4*(3*a^9*b - 4*a^7*b^3 - 14*a^5*b^5 - 4*a^3*b^7 + 3*a*b^9)*c^3*d^3 + 2*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10)*c^2*d^4 - 2*(3*a^9*b - 4*a^7*b^3 - 14*a^5*b^5 - 4*a^3*b^7 + 3*a*b^9)*c*d^5 + (a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^6)*f^7*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + 2*(4*(a^12*b^2 + 3*a^10*b^4 + 2*a^8*b^6 - 2*a^6*b^8 - 3*a^4*b^10 - a^2*b^12)*c^5 - (a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*c^4*d + 8*(a^12*b^2 + 3*a^10*b^4 + 2*a^8*b^6 - 2*a^6*b^8 - 3*a^4*b^10 - a^2*b^12)*c^3*d^2 - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*c^2*d^3 + 4*(a^12*b^2 + 3*a^10*b^4 + 2*a^8*b^6 - 2*a^6*b^8 - 3*a^4*b^10 - a^2*b^12)*c*d^4 - (a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5)*f^5*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(3/4))/(16*(a^22*b^2 + 6*a^20*b^4 + 13*a^18*b^6 + 8*a^16*b^8 - 14*a^14*b^10 - 28*a^12*b^12 - 14*a^10*b^14 + 8*a^8*b^16 + 13*a^6*b^18 + 6*a^4*b^20 + a^2*b^22)*c^2*d - 8*(a^23*b + a^21*b^3 - 21*a^19*b^5 - 85*a^17*b^7 - 134*a^15*b^9 - 70*a^13*b^11 + 70*a^11*b^13 + 134*a^9*b^15 + 85*a^7*b^17 + 21*a^5*b^19 - a^3*b^21 - a*b^23)*c*d^2 + (a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)*d^3)) + 4*sqrt(2)*(c^2*d + d^3)*f^5*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(3/4)*arctan(-((4*(a^15*b + 5*a^13*b^3 + 9*a^11*b^5 + 5*a^9*b^7 - 5*a^7*b^9 - 9*a^5*b^11 - 5*a^3*b^13 - a*b^15)*c^5 - (a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*c^4*d + 8*(a^15*b + 5*a^13*b^3 + 9*a^11*b^5 + 5*a^9*b^7 - 5*a^7*b^9 - 9*a^5*b^11 - 5*a^3*b^13 - a*b^15)*c^3*d^2 - 2*(a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*c^2*d^3 + 4*(a^15*b + 5*a^13*b^3 + 9*a^11*b^5 + 5*a^9*b^7 - 5*a^7*b^9 - 9*a^5*b^11 - 5*a^3*b^13 - a*b^15)*c*d^4 - (a^16 - 20*a^12*b^4 - 64*a^10*b^6 - 90*a^8*b^8 - 64*a^6*b^10 - 20*a^4*b^12 + b^16)*d^5)*f^4*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (4*(a^19*b + 7*a^17*b^3 + 20*a^15*b^5 + 28*a^13*b^7 + 14*a^11*b^9 - 14*a^9*b^11 - 28*a^7*b^13 - 20*a^5*b^15 - 7*a^3*b^17 - a*b^19)*c^4 - (a^20 + 2*a^18*b^2 - 19*a^16*b^4 - 104*a^14*b^6 - 238*a^12*b^8 - 308*a^10*b^10 - 238*a^8*b^12 - 104*a^6*b^14 - 19*a^4*b^16 + 2*a^2*b^18 + b^20)*c^3*d + 4*(a^19*b + 7*a^17*b^3 + 20*a^15*b^5 + 28*a^13*b^7 + 14*a^11*b^9 - 14*a^9*b^11 - 28*a^7*b^13 - 20*a^5*b^15 - 7*a^3*b^17 - a*b^19)*c^2*d^2 - (a^20 + 2*a^18*b^2 - 19*a^16*b^4 - 104*a^14*b^6 - 238*a^12*b^8 - 308*a^10*b^10 - 238*a^8*b^12 - 104*a^6*b^14 - 19*a^4*b^16 + 2*a^2*b^18 + b^20)*c*d^3)*f^2*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)) - sqrt(2)*((2*a*b*c^5 + 4*a*b*c^3*d^2 + 2*a*b*c*d^4 - (a^2 - b^2)*c^4*d - 2*(a^2 - b^2)*c^2*d^3 - (a^2 - b^2)*d^5)*f^7*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + 2*((a^5*b + 2*a^3*b^3 + a*b^5)*c^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*c^2*d^2 + (a^5*b + 2*a^3*b^3 + a*b^5)*d^4)*f^5*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt(((16*(a^10*b^2 - 2*a^6*b^6 + a^2*b^10)*c^4 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c^3*d + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*c^2*d^2 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c*d^3 + (a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^4)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) - sqrt(2)*(2*(16*(a^7*b^3 - 2*a^5*b^5 + a^3*b^7)*c^4 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c^3*d + (a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c*d^3 + (a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^4)*f^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) + (32*(a^11*b^3 - 2*a^7*b^7 + a^3*b^11)*c^3 - 32*(a^12*b^2 - 3*a^10*b^4 - 4*a^8*b^6 + 4*a^6*b^8 + 3*a^4*b^10 - a^2*b^12)*c^2*d + 2*(5*a^13*b - 34*a^11*b^3 + 11*a^9*b^5 + 100*a^7*b^7 + 11*a^5*b^9 - 34*a^3*b^11 + 5*a*b^13)*c*d^2 - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3)*f*cos(f*x + e))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(1/4) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^3 - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c^2*d + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*c*d^2)*cos(f*x + e) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^2*d - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c*d^2 + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*d^3)*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(3/4) - sqrt(2)*((8*(a^8*b^2 + a^6*b^4 - a^4*b^6 - a^2*b^8)*c^6 - 2*(3*a^9*b - 4*a^7*b^3 - 14*a^5*b^5 - 4*a^3*b^7 + 3*a*b^9)*c^5*d + (a^10 + 11*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 - 11*a^2*b^8 - b^10)*c^4*d^2 - 4*(3*a^9*b - 4*a^7*b^3 - 14*a^5*b^5 - 4*a^3*b^7 + 3*a*b^9)*c^3*d^3 + 2*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10)*c^2*d^4 - 2*(3*a^9*b - 4*a^7*b^3 - 14*a^5*b^5 - 4*a^3*b^7 + 3*a*b^9)*c*d^5 + (a^10 - 5*a^8*b^2 - 6*a^6*b^4 + 6*a^4*b^6 + 5*a^2*b^8 - b^10)*d^6)*f^7*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + 2*(4*(a^12*b^2 + 3*a^10*b^4 + 2*a^8*b^6 - 2*a^6*b^8 - 3*a^4*b^10 - a^2*b^12)*c^5 - (a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*c^4*d + 8*(a^12*b^2 + 3*a^10*b^4 + 2*a^8*b^6 - 2*a^6*b^8 - 3*a^4*b^10 - a^2*b^12)*c^3*d^2 - 2*(a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*c^2*d^3 + 4*(a^12*b^2 + 3*a^10*b^4 + 2*a^8*b^6 - 2*a^6*b^8 - 3*a^4*b^10 - a^2*b^12)*c*d^4 - (a^13*b - 2*a^11*b^3 - 17*a^9*b^5 - 28*a^7*b^7 - 17*a^5*b^9 - 2*a^3*b^11 + a*b^13)*d^5)*f^5*sqrt((16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(3/4))/(16*(a^22*b^2 + 6*a^20*b^4 + 13*a^18*b^6 + 8*a^16*b^8 - 14*a^14*b^10 - 28*a^12*b^12 - 14*a^10*b^14 + 8*a^8*b^16 + 13*a^6*b^18 + 6*a^4*b^20 + a^2*b^22)*c^2*d - 8*(a^23*b + a^21*b^3 - 21*a^19*b^5 - 85*a^17*b^7 - 134*a^15*b^9 - 70*a^13*b^11 + 70*a^11*b^13 + 134*a^9*b^15 + 85*a^7*b^17 + 21*a^5*b^19 - a^3*b^21 - a*b^23)*c*d^2 + (a^24 - 4*a^22*b^2 - 30*a^20*b^4 + 12*a^18*b^6 + 367*a^16*b^8 + 1016*a^14*b^10 + 1372*a^12*b^12 + 1016*a^10*b^14 + 367*a^8*b^16 + 12*a^6*b^18 - 30*a^4*b^20 - 4*a^2*b^22 + b^24)*d^3)) + sqrt(2)*(((a^4 - 6*a^2*b^2 + b^4)*c*d + 4*(a^3*b - a*b^3)*d^2)*f^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*f)*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(1/4)*log(((16*(a^10*b^2 - 2*a^6*b^6 + a^2*b^10)*c^4 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c^3*d + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*c^2*d^2 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c*d^3 + (a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^4)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) + sqrt(2)*(2*(16*(a^7*b^3 - 2*a^5*b^5 + a^3*b^7)*c^4 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c^3*d + (a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c*d^3 + (a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^4)*f^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) + (32*(a^11*b^3 - 2*a^7*b^7 + a^3*b^11)*c^3 - 32*(a^12*b^2 - 3*a^10*b^4 - 4*a^8*b^6 + 4*a^6*b^8 + 3*a^4*b^10 - a^2*b^12)*c^2*d + 2*(5*a^13*b - 34*a^11*b^3 + 11*a^9*b^5 + 100*a^7*b^7 + 11*a^5*b^9 - 34*a^3*b^11 + 5*a*b^13)*c*d^2 - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3)*f*cos(f*x + e))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(1/4) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^3 - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c^2*d + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*c*d^2)*cos(f*x + e) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^2*d - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c*d^2 + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*d^3)*sin(f*x + e))/cos(f*x + e)) - sqrt(2)*(((a^4 - 6*a^2*b^2 + b^4)*c*d + 4*(a^3*b - a*b^3)*d^2)*f^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*f)*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(1/4)*log(((16*(a^10*b^2 - 2*a^6*b^6 + a^2*b^10)*c^4 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c^3*d + (a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*c^2*d^2 - 8*(a^11*b - 5*a^9*b^3 - 6*a^7*b^5 + 6*a^5*b^7 + 5*a^3*b^9 - a*b^11)*c*d^3 + (a^12 - 10*a^10*b^2 + 15*a^8*b^4 + 52*a^6*b^6 + 15*a^4*b^8 - 10*a^2*b^10 + b^12)*d^4)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) - sqrt(2)*(2*(16*(a^7*b^3 - 2*a^5*b^5 + a^3*b^7)*c^4 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c^3*d + (a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 - 8*(a^8*b^2 - 7*a^6*b^4 + 7*a^4*b^6 - a^2*b^8)*c*d^3 + (a^9*b - 12*a^7*b^3 + 38*a^5*b^5 - 12*a^3*b^7 + a*b^9)*d^4)*f^3*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))*cos(f*x + e) + (32*(a^11*b^3 - 2*a^7*b^7 + a^3*b^11)*c^3 - 32*(a^12*b^2 - 3*a^10*b^4 - 4*a^8*b^6 + 4*a^6*b^8 + 3*a^4*b^10 - a^2*b^12)*c^2*d + 2*(5*a^13*b - 34*a^11*b^3 + 11*a^9*b^5 + 100*a^7*b^7 + 11*a^5*b^9 - 34*a^3*b^11 + 5*a*b^13)*c*d^2 - (a^14 - 11*a^12*b^2 + 25*a^10*b^4 + 37*a^8*b^6 - 37*a^6*b^8 - 25*a^4*b^10 + 11*a^2*b^12 - b^14)*d^3)*f*cos(f*x + e))*sqrt((((a^4 - 6*a^2*b^2 + b^4)*c^3 + 4*(a^3*b - a*b^3)*c^2*d + (a^4 - 6*a^2*b^2 + b^4)*c*d^2 + 4*(a^3*b - a*b^3)*d^3)*f^2*sqrt((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4)) + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*c^2 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d^2)/(16*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*c^2 - 8*(a^7*b - 7*a^5*b^3 + 7*a^3*b^5 - a*b^7)*c*d + (a^8 - 12*a^6*b^2 + 38*a^4*b^4 - 12*a^2*b^6 + b^8)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)/((c^2 + d^2)*f^4))^(1/4) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^3 - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c^2*d + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*c*d^2)*cos(f*x + e) + (16*(a^14*b^2 + 2*a^12*b^4 - a^10*b^6 - 4*a^8*b^8 - a^6*b^10 + 2*a^4*b^12 + a^2*b^14)*c^2*d - 8*(a^15*b - 3*a^13*b^3 - 15*a^11*b^5 - 11*a^9*b^7 + 11*a^7*b^9 + 15*a^5*b^11 + 3*a^3*b^13 - a*b^15)*c*d^2 + (a^16 - 8*a^14*b^2 - 4*a^12*b^4 + 72*a^10*b^6 + 134*a^8*b^8 + 72*a^6*b^10 - 4*a^4*b^12 - 8*a^2*b^14 + b^16)*d^3)*sin(f*x + e))/cos(f*x + e)) + 8*(a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d*f)","B",0
1250,1,8282,0,9.389336," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(c^{2} + d^{2}\right)} f^{4} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} \arctan\left(\frac{{\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c^{5} - {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{4} d + 4 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c^{3} d^{2} - 2 \, {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{2} d^{3} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c d^{4} - {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{5}\right)} f^{4} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{4} - {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c^{3} d + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} - {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c d^{3}\right)} f^{2} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} - \sqrt{2} {\left({\left(b c^{5} - a c^{4} d + 2 \, b c^{3} d^{2} - 2 \, a c^{2} d^{3} + b c d^{4} - a d^{5}\right)} f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left({\left(a^{2} b + b^{3}\right)} c^{4} + 2 \, {\left(a^{2} b + b^{3}\right)} c^{2} d^{2} + {\left(a^{2} b + b^{3}\right)} d^{4}\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} - 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} - 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{4} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} d + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d^{2} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{3} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} - 4 \, {\left(2 \, a^{5} b^{2} + a^{3} b^{4} - a b^{6}\right)} c^{2} d + {\left(5 \, a^{6} b - a^{4} b^{3} - 5 \, a^{2} b^{5} + b^{7}\right)} c d^{2} - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{3} - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{2} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{6} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} c^{5} d + {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{4} d^{2} - 2 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} c^{3} d^{3} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} c d^{5} + {\left(a^{5} - a b^{4}\right)} d^{6}\right)} f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{5} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} c^{4} d + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d^{2} - 2 \, {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} c^{2} d^{3} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{4} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5}\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}}}{4 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{2} d - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} c d^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d^{3}}\right) + 4 \, \sqrt{2} {\left(c^{2} + d^{2}\right)} f^{4} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} \arctan\left(-\frac{{\left(2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c^{5} - {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{4} d + 4 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c^{3} d^{2} - 2 \, {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} c^{2} d^{3} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} c d^{4} - {\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d^{5}\right)} f^{4} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{4} - {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c^{3} d + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} c^{2} d^{2} - {\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} c d^{3}\right)} f^{2} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} + \sqrt{2} {\left({\left(b c^{5} - a c^{4} d + 2 \, b c^{3} d^{2} - 2 \, a c^{2} d^{3} + b c d^{4} - a d^{5}\right)} f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left({\left(a^{2} b + b^{3}\right)} c^{4} + 2 \, {\left(a^{2} b + b^{3}\right)} c^{2} d^{2} + {\left(a^{2} b + b^{3}\right)} d^{4}\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} - 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} - 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{4} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} d + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d^{2} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{3} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} - 4 \, {\left(2 \, a^{5} b^{2} + a^{3} b^{4} - a b^{6}\right)} c^{2} d + {\left(5 \, a^{6} b - a^{4} b^{3} - 5 \, a^{2} b^{5} + b^{7}\right)} c d^{2} - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{3} - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{2} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} {\left({\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{6} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} c^{5} d + {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} c^{4} d^{2} - 2 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} c^{3} d^{3} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} c d^{5} + {\left(a^{5} - a b^{4}\right)} d^{6}\right)} f^{7} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{5} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} c^{4} d + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{3} d^{2} - 2 \, {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} c^{2} d^{3} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c d^{4} - {\left(a^{6} b + a^{4} b^{3} - a^{2} b^{5} - b^{7}\right)} d^{5}\right)} f^{5} \sqrt{\frac{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} f^{4}}}\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{3}{4}}}{4 \, {\left(a^{10} b^{2} + 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} + 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} c^{2} d - 4 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 2 \, a^{7} b^{5} - 2 \, a^{5} b^{7} - 3 \, a^{3} b^{9} - a b^{11}\right)} c d^{2} + {\left(a^{12} + 2 \, a^{10} b^{2} - a^{8} b^{4} - 4 \, a^{6} b^{6} - a^{4} b^{8} + 2 \, a^{2} b^{10} + b^{12}\right)} d^{3}}\right) - \sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(2 \, a b d + {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}}\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} - 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} - 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{4} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} d + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d^{2} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{3} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} - 4 \, {\left(2 \, a^{5} b^{2} + a^{3} b^{4} - a b^{6}\right)} c^{2} d + {\left(5 \, a^{6} b - a^{4} b^{3} - 5 \, a^{2} b^{5} + b^{7}\right)} c d^{2} - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{3} - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{2} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + \sqrt{2} {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} - {\left(2 \, a b d + {\left(a^{2} - b^{2}\right)} c\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}}\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{4} - 4 \, {\left(a^{5} b - a b^{5}\right)} c^{3} d + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} - 4 \, {\left(a^{5} b - a b^{5}\right)} c d^{3} + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d^{4}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) - \sqrt{2} {\left({\left(4 \, a^{2} b^{3} c^{4} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c^{3} d + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d^{2} - 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c d^{3} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{4}\right)} f^{3} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{4} b^{3} + a^{2} b^{5}\right)} c^{3} - 4 \, {\left(2 \, a^{5} b^{2} + a^{3} b^{4} - a b^{6}\right)} c^{2} d + {\left(5 \, a^{6} b - a^{4} b^{3} - 5 \, a^{2} b^{5} + b^{7}\right)} c d^{2} - {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} f \cos\left(f x + e\right)\right)} \sqrt{\frac{{\left(2 \, a b c^{2} d + 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} + {\left(a^{2} - b^{2}\right)} c d^{2}\right)} f^{2} \sqrt{\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}{4 \, a^{2} b^{2} c^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}} \sqrt{\frac{c \cos\left(f x + e\right) + d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{a^{4} + 2 \, a^{2} b^{2} + b^{4}}{{\left(c^{2} + d^{2}\right)} f^{4}}\right)^{\frac{1}{4}} + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{3} - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c^{2} d + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d - 4 \, {\left(a^{7} b + a^{5} b^{3} - a^{3} b^{5} - a b^{7}\right)} c d^{2} + {\left(a^{8} - 2 \, a^{4} b^{4} + b^{8}\right)} d^{3}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)}{4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/4*(4*sqrt(2)*(c^2 + d^2)*f^4*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(3/4)*arctan(((2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c^5 - (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^4*d + 4*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c^3*d^2 - 2*(a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^2*d^3 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c*d^4 - (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^5)*f^4*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^4 - (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c^3*d + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 - (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c*d^3)*f^2*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)) - sqrt(2)*((b*c^5 - a*c^4*d + 2*b*c^3*d^2 - 2*a*c^2*d^3 + b*c*d^4 - a*d^5)*f^7*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + ((a^2*b + b^3)*c^4 + 2*(a^2*b + b^3)*c^2*d^2 + (a^2*b + b^3)*d^4)*f^5*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt(((4*(a^4*b^2 + a^2*b^4)*c^4 - 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 - 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) + sqrt(2)*((4*a^2*b^3*c^4 - 4*(a^3*b^2 - a*b^4)*c^3*d + (a^4*b + 2*a^2*b^3 + b^5)*c^2*d^2 - 4*(a^3*b^2 - a*b^4)*c*d^3 + (a^4*b - 2*a^2*b^3 + b^5)*d^4)*f^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^3 - 4*(2*a^5*b^2 + a^3*b^4 - a*b^6)*c^2*d + (5*a^6*b - a^4*b^3 - 5*a^2*b^5 + b^7)*c*d^2 - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3)*f*cos(f*x + e))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^3 - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d + (a^8 - 2*a^4*b^4 + b^8)*c*d^2)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2*d - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^2 + (a^8 - 2*a^4*b^4 + b^8)*d^3)*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(3/4) + sqrt(2)*((2*(a^3*b^2 + a*b^4)*c^6 - (3*a^4*b + 2*a^2*b^3 - b^5)*c^5*d + (a^5 + 4*a^3*b^2 + 3*a*b^4)*c^4*d^2 - 2*(3*a^4*b + 2*a^2*b^3 - b^5)*c^3*d^3 + 2*(a^5 + a^3*b^2)*c^2*d^4 - (3*a^4*b + 2*a^2*b^3 - b^5)*c*d^5 + (a^5 - a*b^4)*d^6)*f^7*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^5 - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*c^4*d + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^3*d^2 - 2*(a^6*b + a^4*b^3 - a^2*b^5 - b^7)*c^2*d^3 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c*d^4 - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5)*f^5*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(3/4))/(4*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*c^2*d - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*c*d^2 + (a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)*d^3)) + 4*sqrt(2)*(c^2 + d^2)*f^4*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(3/4)*arctan(-((2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c^5 - (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^4*d + 4*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c^3*d^2 - 2*(a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*c^2*d^3 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*c*d^4 - (a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d^5)*f^4*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^4 - (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c^3*d + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*c^2*d^2 - (a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*c*d^3)*f^2*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)) + sqrt(2)*((b*c^5 - a*c^4*d + 2*b*c^3*d^2 - 2*a*c^2*d^3 + b*c*d^4 - a*d^5)*f^7*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + ((a^2*b + b^3)*c^4 + 2*(a^2*b + b^3)*c^2*d^2 + (a^2*b + b^3)*d^4)*f^5*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt(((4*(a^4*b^2 + a^2*b^4)*c^4 - 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 - 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) - sqrt(2)*((4*a^2*b^3*c^4 - 4*(a^3*b^2 - a*b^4)*c^3*d + (a^4*b + 2*a^2*b^3 + b^5)*c^2*d^2 - 4*(a^3*b^2 - a*b^4)*c*d^3 + (a^4*b - 2*a^2*b^3 + b^5)*d^4)*f^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^3 - 4*(2*a^5*b^2 + a^3*b^4 - a*b^6)*c^2*d + (5*a^6*b - a^4*b^3 - 5*a^2*b^5 + b^7)*c*d^2 - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3)*f*cos(f*x + e))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^3 - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d + (a^8 - 2*a^4*b^4 + b^8)*c*d^2)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2*d - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^2 + (a^8 - 2*a^4*b^4 + b^8)*d^3)*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(3/4) - sqrt(2)*((2*(a^3*b^2 + a*b^4)*c^6 - (3*a^4*b + 2*a^2*b^3 - b^5)*c^5*d + (a^5 + 4*a^3*b^2 + 3*a*b^4)*c^4*d^2 - 2*(3*a^4*b + 2*a^2*b^3 - b^5)*c^3*d^3 + 2*(a^5 + a^3*b^2)*c^2*d^4 - (3*a^4*b + 2*a^2*b^3 - b^5)*c*d^5 + (a^5 - a*b^4)*d^6)*f^7*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4))*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^5 - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*c^4*d + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^3*d^2 - 2*(a^6*b + a^4*b^3 - a^2*b^5 - b^7)*c^2*d^3 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c*d^4 - (a^6*b + a^4*b^3 - a^2*b^5 - b^7)*d^5)*f^5*sqrt((4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2)/((c^4 + 2*c^2*d^2 + d^4)*f^4)))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(3/4))/(4*(a^10*b^2 + 4*a^8*b^4 + 6*a^6*b^6 + 4*a^4*b^8 + a^2*b^10)*c^2*d - 4*(a^11*b + 3*a^9*b^3 + 2*a^7*b^5 - 2*a^5*b^7 - 3*a^3*b^9 - a*b^11)*c*d^2 + (a^12 + 2*a^10*b^2 - a^8*b^4 - 4*a^6*b^6 - a^4*b^8 + 2*a^2*b^10 + b^12)*d^3)) - sqrt(2)*(a^4 + 2*a^2*b^2 + b^4 - (2*a*b*d + (a^2 - b^2)*c)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(1/4)*log(((4*(a^4*b^2 + a^2*b^4)*c^4 - 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 - 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) + sqrt(2)*((4*a^2*b^3*c^4 - 4*(a^3*b^2 - a*b^4)*c^3*d + (a^4*b + 2*a^2*b^3 + b^5)*c^2*d^2 - 4*(a^3*b^2 - a*b^4)*c*d^3 + (a^4*b - 2*a^2*b^3 + b^5)*d^4)*f^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^3 - 4*(2*a^5*b^2 + a^3*b^4 - a*b^6)*c^2*d + (5*a^6*b - a^4*b^3 - 5*a^2*b^5 + b^7)*c*d^2 - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3)*f*cos(f*x + e))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^3 - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d + (a^8 - 2*a^4*b^4 + b^8)*c*d^2)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2*d - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^2 + (a^8 - 2*a^4*b^4 + b^8)*d^3)*sin(f*x + e))/cos(f*x + e)) + sqrt(2)*(a^4 + 2*a^2*b^2 + b^4 - (2*a*b*d + (a^2 - b^2)*c)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(1/4)*log(((4*(a^4*b^2 + a^2*b^4)*c^4 - 4*(a^5*b - a*b^5)*c^3*d + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 - 4*(a^5*b - a*b^5)*c*d^3 + (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d^4)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) - sqrt(2)*((4*a^2*b^3*c^4 - 4*(a^3*b^2 - a*b^4)*c^3*d + (a^4*b + 2*a^2*b^3 + b^5)*c^2*d^2 - 4*(a^3*b^2 - a*b^4)*c*d^3 + (a^4*b - 2*a^2*b^3 + b^5)*d^4)*f^3*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))*cos(f*x + e) + (4*(a^4*b^3 + a^2*b^5)*c^3 - 4*(2*a^5*b^2 + a^3*b^4 - a*b^6)*c^2*d + (5*a^6*b - a^4*b^3 - 5*a^2*b^5 + b^7)*c*d^2 - (a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d^3)*f*cos(f*x + e))*sqrt(((2*a*b*c^2*d + 2*a*b*d^3 + (a^2 - b^2)*c^3 + (a^2 - b^2)*c*d^2)*f^2*sqrt((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4)) + (a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)/(4*a^2*b^2*c^2 - 4*(a^3*b - a*b^3)*c*d + (a^4 - 2*a^2*b^2 + b^4)*d^2))*sqrt((c*cos(f*x + e) + d*sin(f*x + e))/cos(f*x + e))*((a^4 + 2*a^2*b^2 + b^4)/((c^2 + d^2)*f^4))^(1/4) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^3 - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c^2*d + (a^8 - 2*a^4*b^4 + b^8)*c*d^2)*cos(f*x + e) + (4*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2*d - 4*(a^7*b + a^5*b^3 - a^3*b^5 - a*b^7)*c*d^2 + (a^8 - 2*a^4*b^4 + b^8)*d^3)*sin(f*x + e))/cos(f*x + e)))/(a^4 + 2*a^2*b^2 + b^4)","B",0
1251,-1,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1252,-1,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1253,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1254,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1256,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1257,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1258,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1259,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1260,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1261,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1262,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1263,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1264,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1265,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1266,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1267,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1268,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1269,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1270,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1271,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1273,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1274,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1275,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1276,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1277,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1278,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1279,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1280,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1281,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1282,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1283,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1284,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1285,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1286,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1287,-1,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1288,-1,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1289,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1290,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1291,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1292,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1293,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1294,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1295,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1296,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(9/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1300,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1301,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1302,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1303,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1304,0,0,0,1.463892," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)}^{m} {\left(d \tan\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m*(d*tan(f*x + e) + c)^n, x)","F",0
1305,0,0,0,1.132392," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{3} \tan\left(f x + e\right)^{3} + 3 \, c d^{2} \tan\left(f x + e\right)^{2} + 3 \, c^{2} d \tan\left(f x + e\right) + c^{3}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((d^3*tan(f*x + e)^3 + 3*c*d^2*tan(f*x + e)^2 + 3*c^2*d*tan(f*x + e) + c^3)*(b*tan(f*x + e) + a)^m, x)","F",0
1306,0,0,0,0.983134," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2)*(b*tan(f*x + e) + a)^m, x)","F",0
1307,0,0,0,1.003559," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d \tan\left(f x + e\right) + c\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m, x)","F",0
1308,0,0,0,0.633936," ","integrate((a+b*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m, x)","F",0
1309,0,0,0,0.783988," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d \tan\left(f x + e\right) + c}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c), x)","F",0
1310,0,0,0,0.940400," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m/(d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2), x)","F",0
1311,0,0,0,0.911528," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d^{3} \tan\left(f x + e\right)^{3} + 3 \, c d^{2} \tan\left(f x + e\right)^{2} + 3 \, c^{2} d \tan\left(f x + e\right) + c^{3}}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m/(d^3*tan(f*x + e)^3 + 3*c*d^2*tan(f*x + e)^2 + 3*c^2*d*tan(f*x + e) + c^3), x)","F",0
1312,0,0,0,1.077402," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((d*tan(f*x + e) + c)^(3/2)*(b*tan(f*x + e) + a)^m, x)","F",0
1313,0,0,0,0.968998," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right) + c} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m, x)","F",0
1314,0,0,0,1.200731," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \tan\left(f x + e\right) + c}}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)^m/sqrt(d*tan(f*x + e) + c), x)","F",0
1315,0,0,0,1.300393," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right) + c} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d^{2} \tan\left(f x + e\right)^{2} + 2 \, c d \tan\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m/(d^2*tan(f*x + e)^2 + 2*c*d*tan(f*x + e) + c^2), x)","F",0
1316,0,0,0,1.635372," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right) + c} {\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d^{3} \tan\left(f x + e\right)^{3} + 3 \, c d^{2} \tan\left(f x + e\right)^{2} + 3 \, c^{2} d \tan\left(f x + e\right) + c^{3}}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m/(d^3*tan(f*x + e)^3 + 3*c*d^2*tan(f*x + e)^2 + 3*c^2*d*tan(f*x + e) + c^3), x)","F",0
1317,0,0,0,1.280867," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, f x + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{m} e^{\left(n p \log\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) + n \log\left(c\right)\right)}, x\right)"," ",0,"integral((2*a*e^(2*I*f*x + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1))^m*e^(n*p*log((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + n*log(c)), x)","F",0
1318,0,0,0,1.349840," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, a^{3} e^{\left(n p \log\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) + 6 i \, f x + n \log\left(c\right) + 6 i \, e\right)}}{e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(8*a^3*e^(n*p*log((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + 6*I*f*x + n*log(c) + 6*I*e)/(e^(6*I*f*x + 6*I*e) + 3*e^(4*I*f*x + 4*I*e) + 3*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1319,0,0,0,0.695066," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, a^{2} e^{\left(n p \log\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) + 4 i \, f x + n \log\left(c\right) + 4 i \, e\right)}}{e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(4*a^2*e^(n*p*log((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + 4*I*f*x + n*log(c) + 4*I*e)/(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1320,0,0,0,0.833300," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a e^{\left(n p \log\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) + 2 i \, f x + n \log\left(c\right) + 2 i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}, x\right)"," ",0,"integral(2*a*e^(n*p*log((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) + 2*I*f*x + n*log(c) + 2*I*e)/(e^(2*I*f*x + 2*I*e) + 1), x)","F",0
1321,0,0,0,0.693323," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(n p \log\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - 2 i \, f x + n \log\left(c\right) - 2 i \, e\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*(e^(2*I*f*x + 2*I*e) + 1)*e^(n*p*log((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) - 2*I*f*x + n*log(c) - 2*I*e)/a, x)","F",0
1322,0,0,0,0.705439," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(n p \log\left(\frac{-i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + i \, d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - 4 i \, f x + n \log\left(c\right) - 4 i \, e\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*(e^(4*I*f*x + 4*I*e) + 2*e^(2*I*f*x + 2*I*e) + 1)*e^(n*p*log((-I*d*e^(2*I*f*x + 2*I*e) + I*d)/(e^(2*I*f*x + 2*I*e) + 1)) - 4*I*f*x + n*log(c) - 4*I*e)/a^2, x)","F",0
1323,0,0,0,0.698631," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n} {\left(b \tan\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(((d*tan(f*x + e))^p*c)^n*(b*tan(f*x + e) + a)^m, x)","F",0
1324,0,0,0,0.874644," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*((d*tan(f*x + e))^p*c)^n, x)","F",0
1325,0,0,0,0.531668," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*((d*tan(f*x + e))^p*c)^n, x)","F",0
1326,0,0,0,0.475231," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)*((d*tan(f*x + e))^p*c)^n, x)","F",0
1327,0,0,0,0.713835," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}}{b \tan\left(f x + e\right) + a}, x\right)"," ",0,"integral(((d*tan(f*x + e))^p*c)^n/(b*tan(f*x + e) + a), x)","F",0
1328,0,0,0,0.709746," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}}{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(((d*tan(f*x + e))^p*c)^n/(b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2), x)","F",0
